"You'll soon find out some wizarding families are much better than others, Potter. You don't want to go making friends with the wrong sort."
Draco Malfoy is the only son of Lucius and Narcissa Malfoy and he is a pure-blood wizard. His father served the dark wizard Voldemort, making Draco the son of a Death Eater. However, Voldemort vanished at the hands of Harry Potter who was only an infant at the time, making the boy an instant legend and hero.
Draco started attending Hogwarts School of Witchcraft and Wizardry at the age of eleven and was put into Slytherin house immediately, like the rest of his family. Slytherin house is known for being the house of Voldemort, so they are instantly pegged as the bad guys by everyone else in the wizarding society. However, it is also the same house as the most famous and powerful wizard in history, Merlin, who was a muggle sympathizer. While the Slytherin's take pride in this fact, the other houses choose to ignore it. Draco became easy friends with two other Slytherins: Vincent Crabbe and Gregory Goyle, both with fathers who were Death Eaters. The Malfoy family is very rich and powerful (as was Narcissa's family, the Blacks), but their prejudice for anyone not having full wizard blood made Draco not only seem imposing to other students, but also demeaning and difficult to approach.
During his first year at Hogwarts, Draco met Harry Potter while being fitted for robes, though he didn't realize who it was at the time. The two had a decent enough conversation in which Draco was polite to Harry, but continued to demean others that were lower than the pure-blood status. While on the train to Hogwarts, Draco approached Harry again, but Potter shot down his offer of friendship since the other was rude to his newest friend, Ron Weasley, for being poor.
Since then Harry and Draco have become rivals. Soon after, Harry had shown astounding flying abilities on the broom and was allowed to join Gryffindor's Quidditch team, even though he was only a first year student. This, coupled with many other achievements from Potter, made Draco jealous so he tried to get Harry in trouble. The first attempt failed, but the second landed them both in detention, where Draco had to help Harry and his friends with the task of helping a unicorn that was about to be killed by some other being. Draco and Harry went off together. When confronted with the creature, Draco immediately screamed and ran while Harry simply remained motionless. Once Draco had gotten Hagrid and returned to Harry, the being was gone.
Draco's first year finished without any other incidents, except for rumors of what Harry Potter and his friends did concerning Lord Voldemort and their former Defense Against the Dark Arts teacher. During the second year, Draco had been made Slytherin's newest Seeker and his father, in celebration of the event, got the entire team brand new broomsticks. Hermonie Granger remarked that Harry got on his team by skill and not bribery (which may not be entirely true, considering who Harry Potter is, even if it was unintentional). Draco shot back that Hermonie was nothing more than a "Mudblood" which got an instant, violent response from the surrounding Gryffindors. Ron even tried to hex Draco, but it backfired on to him due to his broken wand. It is later made known that "Mudblood" is an insulting term aimed for someone that is not a pure-blood wizard. Hermonie Granger was born from Muggle (non-magical) parents, which makes Draco hate her even more.
Lucius came out to oversee Draco's first Quidditch game against Gryffindor, but ended up sorely disappointed in his son when he lost the snitch to Harry in a quite embarrassing way. He was even reprimanded by the team captain for his failure and arrogance during the match. Later, Draco found a way to take revenge on Potter in a Wizarding Duel. During this, he conjured a snake and revealed to everyone there that Harry was a Parseltongue (someone who could talk to snakes). Considering that this skill belonged to Voldemort before, this was quite a blow to Harry. This event led some to believe that Harry was the heir of Slytherin and could access the legendary Chamber of Secrets, even though Harry suspected that Draco was the heir.
Harry and Ron used a Polyjuice Potion to take on the form of Crabbe and Goyle. With this, they infiltrated the Slytherin common room with an unknowing Draco. During the following conversation between the three, they learned that Draco was not only disproving that he was the heir of Slytherin, but also didn't start the rumors that Harry was either. In fact, he firmly believed that Harry wasn't and would oppose anyone who thought otherwise. As it turned out, it was Lucius who wanted to open the chamber from the beginning by placing a book accidentally with Ginny Weasley that was intended for her father. It is believed that Draco was unaware of anything that his father planned.
The book turned out to be Tom Riddle's (aka, Voldemort's) diary and one of his Horcruxes. A Horcrux is an item that one can put their soul into to prevent death. Harry Potter, at the end of their second year, destroyed the book.
Their third year began with the escape of Sirius Black from Azkaban prison. Because of this and the belief that Harry may be a target for Sirius considering it had been believed that he killed Harry's parents, Dementors began patrolling the school. Dementors are creatures that feed off of happiness, leaving people only with despair. They were the guards of Azkaban prison and sought out their targets of escapees, but would also destroy anyone in their way.
Harry had an early encounter with the Dementors and ended up passing out from their presence. Draco used this to mock Harry whenever he could get the chance, even despite the fact that everyone was actually scared of the things, including Draco himself. Once this became old, Draco began berating Potter and telling him that if his parents were killed and the murderer was on the loose, he would seek revenge. While Draco is a coward and would probably hide just like Harry was doing, it's no doubt that he meant his words and looks down on Harry for not doing so. During Harry's Quidditch match against Ravenclaw, Draco took it one step further by getting himself and his friends dressed up as Dementors to scare Potter. This failed when Harry knocked them all over with the Patronus Charm.
Later, Harry got to ride on the hippogriff, Buckbeak, during their Care of Magical Creatures class. This angered Draco because, once again, Potter was getting the spotlight for doing something that anyone could do. He then approached Buckbeak, but did it wrong and ended up injured by the creature. Though the injury wasn't bad, Lucius took immediate action with the Ministry of Magic over this incident and tried to get the teacher, Rubeus Hagrid, fired. This fell through, but all agreed to execute Buckbeak for hurting someone. Later, Harry and Hermonie saved Buckbeak by setting him loose from Hogwarts.
During the break, Draco went to the Quidditch World Cup with his father and watched from the Minister of Magic's luxury box. He mocked Harry, Ron, and Hermonie when they crossed paths, flaunting his wealth and pure-blood line, as usual. The games were interrupted by Death Eaters showing up and terrorizing the audience.
Not long after the incident, the fourth year of Hogwarts began, along with the Triwizard Tournament. Harry, even though it was illegal for him to participate in the games, also got to compete. This obviously made Draco very angry, so he quickly began supporting the other champion from Hogwarts, a Hufflepuff named Cedric Diggory. He also became on informer to Rita Skeeter who wrote scandalous articles for the Daily Prophet. This all just angered Potter further and put him on edge with Draco again. Harry even made a remark about Draco’s father and Draco tried to hex him from behind for it, but Malfoy quickly found he had been transfigured into a ferret and was bounced around the room by Barty Crouch Jr. (who was in disguise as Mad-Eye Moody). Professor McGonagall fixed the situation, but the damage had been done. Ron gave him the nickname "The Amazing Bouncing Ferret" and the other students would tease him by saying that Moody was behind him, which would cause Draco to freak out every time.
At the end of the year, with Harry saying that Voldemort had returned and that Diggory had been killed, Draco mocked him for siding against Voldemort. He was hit with several curses by the surrounding crowd.
On their fifth year of Hogwarts, the school had been infiltrated by the Ministry of Magic. One of their own, Dolores Umbridge, began teaching the Defense Against the Dark Arts position. Draco also became a Slytherin prefect during this time. Gryffindor's prefects were Hermonie and Ron, so Draco mocked Harry for not getting the job as often as he could. Ron also became the Gryffindor Keeper for Quidditch. Draco wrote an insulting song for it and also insulted Ron's parents and Harry's mother. This led to Harry and George Weasley to start a fight with Draco and resulted in both Gryffindor's (and Fred Weasley) into being banned from Quidditch for the rest of the year.
Later, Draco became a part of Umbridge's Inquisitorial Squad which was a group that held certain powers over other students once she became Headmaster and Dumbledore had been kicked out of office. Draco then discovered that Harry’s group had started "Dumbledore's Army" which were lessons in the Dark Arts to fight against Voldemort. He exposed the group (Harry, Ron, Hermonie, Ginny, Neville, and Luna) and ended up bringing them all to Umbridge's office. Hermonie lied and told Umbridge that they were trying to contact Dumbledore, so that Umbridge wouldn't use a torturing curse on Harry. Umbridge went alone with Harry and Hermonie to the Forbidden Forest where an alleged weapon had been kept and left the rest in the hands of her squad. Once she left, the remaining "D.A." members made quick work of Draco and his cohorts and left for the battle at the Department of Mysteries in the Ministry of Magic.
Lucius fought with the Death Eaters during this fight and was sent to Azkaban prison soon after. Draco does not realize this fact, nor does he realize that he is about to become a Death Eater himself. Draco will Wake into Nautilus once he realizes that Harry and his group made it off of school grounds.
Draco has many labels and to most he is seen as the outright "bad guy" of the series. However, once the series is shown through his point of view, it is quite a different story.
Draco was raised into a very wealthy, very powerful, and very feared family. He was brought up with the firm belief that he was better than most people and that his father was better than everyone. He didn't exactly grow up in a warm and happy home, instead being chastised to be perfect and not having to work for anything he wanted. Draco grew up spoiled, arrogant, and stunted when it came to the things like compassion and love. He knew that his family cared for him, but it was more of a faith in one another than any actual smiles or words.
He grew up a bit lonely as well. Being as arrogant as he is, Draco didn't have very many equals during his youth. Everyone else was simply below him if they were a part of his peers. Unfortunately, being cut off from others emotionally and becoming more and more spoiled as his childhood went on left him being a "momma’s boy" and an all-around coward. This left his father to chastise him more and for Draco to feel as a disappointment to his father. From that time on, he began striving to do anything to please Lucius.
Then, Harry Potter showed up. Potter had to do absolutely nothing except sit back and allow people to love him and want to be like him. He was famous at a young age for just being absolutely normal and this fact burned Draco. After striving so hard to get acceptance from his father, he is now being compared constantly to "the boy who lived" and has no chance of ever besting what Potter had been able to do as an infant. Draco can see right through him, though. Just like a lot of Harry's peers, he knows that Harry is nothing more than an average kid with few talents and he continues to try and prove it to everyone else. All attempts end in failure, sometimes even embarrassingly so. This only made his jealousy and hatred worse as his father's feelings of disappointment in his son just grew stronger. At least, they did in Draco's eyes.
This led Draco to being more and more vicious with his taunts towards Potter, but it wasn't just him. Draco despised anyone, witch or wizard, who wasn't of a pure-blood line and resented those that were pure-blood but still treated anyone lower of this blood status as equals. His hatred even extends to Headmaster Dumbledore, though this is mostly because the man is hated by the Malfoy family for being on the other side during the first war against Voldemort.
Even though Draco can be a coward and a bully, he is also very smart and has a sharp mind. He had even shown skill with Occlumency (later on in the series), which is a power that allows one to see inside someone else's mind and memories. However, this is due to his ability to dull away the good sides of himself in order to not feel sympathy or compassion to others, which was frowned upon in his family of Death Eaters. Despite that, he does care about his friends; though he's very loathe to admit it. In the end, he's just another kid put into the middle of what his family wants him to be. Unfortunately, he just cannot ever seem to reach the mark that he needs to. Later on, this causes a strong shift in Draco’s character.
Even though anyone can be powerful, pure-blood or not, Draco really is a powerful, pure-blood wizard. Along with the ability to wield magic with a wand and his exceptional skill with flying on a broomstick, this is a list of other, more special abilities he has at this point in time. (See Sources for where most of this information is from.)
Potions - Draco became adept with potion making at a very young age. This could be due to Professor Snape favoring him and possibly giving him extra tutoring, but he still excelled in the subject beyond most of his other peers.
Non-Verbal Magic - Unlike most his age, Draco learned and mastered non-verbal magic at a young age, particularly against jinxes. This takes a lot of skill to do and most under the age of sixteen can't do it at all.
Duelling - Probably due to his family, Draco was an amazing duelist. He dueled against Harry Potter in their second year, using powerful and advanced spells during the match. Later on in his years, he was even able to disarm Dumbledore, though he was distracted at the time.
During his later years, Draco becomes a very powerful wizard, but only because of a very dark purpose. As of now, this is where his strengths lie.