There's actually a discussion board conversation currently going on here at enotes, where you could find numerous answers to your question. I'll try to find the link for you and include it below.
In short, Tom is a former college football star who played at an extremely high level. He has had similar success in business, and in the novel's present he is extremely wealthy. He is outgoing to the point of beligerance, and tends to try to impose his will on others. He can also be abusive.
Tom is also somewhat simple minded and is not a deep thinker. He latches on to theories that support his worldview, rational or not. He is also sexist and self-centered.
One specific moment in the novel that concerns Tom is telling. Tom, who is seeing another woman, is truly surprised and shocked when he finds out that his wife, Daisy, and Gatsby have feelings for each other. It is a moving scene, and reveals just how self-centered Tom is. He just never would have thought that a woman of his could want to go out on him.
There's more to Tom than what I've written. I'm sure other editors will add to it.
Most people would say that Tom Buchanan is the bad guy in this story. He is the least likeable major character in the book, in my opinion.
He is a very arrogant man -- he is arrogant about his body and his athletic talent, he is arrogant about his money and he is arrogant about his race.
He is also very bad to his wife. He seems to regard her more as property to be protected than someone to actually love. We see how he cheats on her, but then we also see how angry he gets when he thinks Gatsby is moving in on Daisy.