Harry's Muggle uncle, Mr. Dursley, is described right out of the gate as "a big, beefy man with hardly any neck, although he did have a very large mustache" (1.2). He and his wife Petunia obsess over their only child, Dudley, and think "there [is] no finer boy anywhere" (1.2). That he thinks so highly of the obnoxious Dudley speaks volumes about what Mr. Dursley is really like.
Mr. Dursley and his wife don't know a lot about the world of magic, but they do their best to keep whatever connection they have to it a secret. They also go out of their way to ignore any signs of magic or wizards that enter into their world on Privet Drive. That's part of the reason they dislike Harry so much – his presence is a constant reminder of the secrets they're keeping and of the family they'd rather forget about. Often it seems like they'd like to forget Harry too:
The Dursleys often spoke about Harry like this, as though he wasn't there – or rather, as though he was something very nasty that couldn't understand them, like a slug. (2.38)
Mr. Dursley also commits mail fraud over and over by keeping Harry from reading his Hogwarts admittance letters. It's a crime to keep someone's mail from him or her, even if he is Harry's legal guardian. The lengths he goes to, trying to keep the magic mail from Harry, are kind of crazy – nailing their mailbox shut, taking the family on a wild goose chase in hopes of escaping the magic mail delivery, and eventually sticking them on a dangerous island in the middle of a storm. Even when Hagrid appears to tell Harry the truth and forcibly make sure he receives the acceptance letter, Mr. Dursley is rude and ignorant, insulting Harry's parents, magic, Hogwarts, and Dumbledore – which really bugs Hagrid. Overall, he refuses believe that Harry's acceptance at Hogwarts is something to be celebrated rather than feared.