Mrs. Norris is a dust colored cat with lamp-like yellow eyes and a skeletal build. Mrs. Norris prowls the corridors of Hogwarts, ever on the lookout for miscreants and mischief-makers.
Mrs. Norris was temporarily Petrified during the 1992-1993 school year when the Basilisk attacked her. It is the fond wish of many of the students to give the meddlesome, tattling Mrs. Norris a good solid kick, but so far no one has carried out this wish because of their fear of Filch. Harry was unsure during his first year as to whether invisibility cloaks work on cats (PS16), but judging from the fact that she was tracking him by scent when he worked on the egg clue (GF25), it would seem that she cannot see through them.
The name Mrs. Norris comes from one of JKR's favorite Jane Austen books, Mansfield Park. In that book, Mrs. Norris is the busybody aunt of the main character who interferes and pokes her nose into other people's business.
J.K. Rowling has confirmed via twitter that Mrs Norris is not part kneazle.