(Click the character infographic to download.)
Vernon Dursley is Harry's horrible uncle. He works for a drill company called Grunnings. On July 31st (Harry's birthday, conveniently forgotten by the Dursleys), Uncle Vernon invites Mr. Mason to Number 4, Privet Drive, Little Whinging, Surrey (his home). Uncle Vernon's plan is to wine and dine Mr. and Mrs. Mason in order to secure a huge order for his drill company. He recruits his wife to do the cooking and entertaining and his son to do the flattering. His nephew, though, he commands to stay in his room making no noise and pretending not to exist. Uncle Vernon thinks Harry is a freak and a trouble-maker because he is a wizard, so he does his best to ignore Harry or lock him away in order to clamp down on Harry's magical tendencies.
When Dobby the house-elf destroys Petunia Dursley's carefully prepared dessert and leaves Harry to take the blame for it, Uncle Vernon tells the Masons that Harry is mentally disturbed. He might almost have been able to close his deal anyway, if there hadn't been an owl post delivery right in his living room. Mrs. Mason is terrified of birds, so she runs out of the Dursleys' house screaming. Uncle Vernon blames Harry for ruining his deal with the Masons. He reads the letter the owl has delivered – it's a warning from the Ministry not to perform magic underage – and realizes that Harry is essentially powerless, because if he does magic he'll be expelled from Hogwarts anyway. So Uncle Vernon seizes the opportunity to go further than he ever has before: he locks Harry in his bedroom with a small cat flap in the door so that Harry can receive (scanty) meals. He also installs bars on Harry's windows so that Harry can't fly away.
There's a lot about Uncle Vernon we don't get – we can't imagine how you could treat a kid the way he treats Harry. What we really don't understand is, if he hates Harry so very much, why does he decide to trap Harry in his own house? What does he hope to achieve by locking Harry away? It makes no sense, but then again, he's totally insane, so we guess that's par for the course.