The Dursleys are Harry's only relatives and they are muggles. Harry was left to live with them when his parents died.
Aunt Petunia is Mrs Potter's sister but they hadn't talked in several years. Uncle Dursley is a big beefy man who's the director of a firm called Grunnings, which makes drills. And of course,there's their son Dudley who is the size of a baby killer whale.
The Dursley's treat Harry horribly since they hate magical (or "abnormal") people. They tried to stop Harry from going to Hogwarts School but they weren't able to since Hagrid came and saved Harry.
The Dursley's live in 4 Privet Drive, Surrey in the most cleaned house because Aunt Petunia simply doesn't tolerate even the tiniest dust particle in the furniture. They had made Harry sleep in the cupboard under the stairs from 11 years and it wasn't until the letters from Hogwarts came, that the Dursleys moved all his stuff in Dudley's second bedroom on the second floor.
Whenever the Dursleys went out somewhere, they always left Harry with Mrs Figg, a mad old lady who lived two streets away, who owned lots of cats and who's also going to be a very important character in book five.