(Click the character infographic to download.)
House: Slytherin, 3rd Year
Draco is not in this book a lot, aside from making some token appearances where he bullies the Gryffindors, especially Harry. In typical Draco fashion, he manages to cause a lot of problems with the page-time he's given: he's responsible for putting Buckbeak on trial after the hippogriff justifiably attacked him, he milks his injury from Buckbeak and screws up the Quidditch match schedule, and he mercilessly teases Harry for his reaction to the Dementors. Malfoy and his ever-present cronies, Crabbe and Goyle, even go so far as to dress up as Dementors at a Quidditch match, in an effort to throw Harry off his game. Harry had been working on his Patronus charm, though, and Malfoy & Co. got what was coming to them. One of the most notable Malfoy moments is where he hints that he knows all about Sirius Black (7.1.48).
However, Malfoy's father clearly lied to him, or didn't know the full truth himself since Sirius wasn't a traitor at all. Perhaps Draco himself knew the truth about Black, courtesy of Malfoy Senior, and opted to provoke Harry with the commonly accepted story of Sirius-as-traitor. It's a bit of a mystery, at any rate.
Our favorite Malfoy scene in the book doesn't require that much thought, though. The scene is, of course, Malfoy getting punched by Hermione. Not only is that a major character moment for Hermione, demonstrating how bold and even reckless she can become at times, but it's also a major moment for Draco, who opts to walk away rather than risk a huge altercation with Hermione (and Ron and Harry). We're starting to see some cracks in Malfoy's façade here – he isn't as all-knowing or all-powerful as he acts, and the Gryffindors get the best of him throughout this novel.