Dudley is the annoying, spoiled son of Mr. and Mrs. Dursley. He's Harry's cousin, but the two couldn't be more different:
Dudley was very fat and hated exercise – unless of course it involved punching somebody. Dudley's favorite punching bag was Harry, but he couldn't often catch him. Harry didn't look it, but he was very fast. (2.14)
In other words, Dudley is an overfed, cruel little boy who takes his favored status for granted and makes fun of his orphaned cousin any chance he gets. He has two bedrooms, while Harry sleeps with spiders in a cramped closet under the stairs. Dudley throws a fit when he gets 36 birthday presents instead of 38. Harry spends the summer before going to Hogwarts trying to stay out of Dudley's way, but later realizes that handling Dudley has prepared him in a twisted sort of way for dealing with other, bigger bullies like Malfoy.
In a sense, Dudley and his parents represent many of the things that are wrong with Muggle England. They're mean, they play favorites, and they have no imaginations. Even when they're confronted with proof of magical powers, they resent them and try to hide from them. They see magic as something to be feared rather than something to be celebrated.