Severus Snape has been lobbying for the position of
Defence Against the Dark Arts teacher since the beginning of the books, but
Professor Dumbledore, the headmaster, refuses to give it to him. His reasoning is not directly explained, but the simplest answer is that Snape is the best
Potions teacher they've ever had and would be hard to replace if he took a different role.
He is unfair in his treatment of students, penalizing those of Gryffindor in every way he can think of (in once case, he docked them points because Hermione Granger helped Neville Longbottom fix his potion, but he would have docked some anyway and hurt Neville's toad if she had not) and showing favoritism to those of Slytherin, his own house.
WARNING: DO NOT READ THIS PARAGRAPH UNLESS YOU ALREADY KNOW THE END OF BOOK ONE!
Although he is a very suspicious and underhanded person, Snape is completely loyal to Hogwarts and to the good side. In Harry Potter and the Sorceror's Stone, the kids suspected him of working with Voldemort, but it turned out he not only wasn't, but he was actively trying to stop the person who was.
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In the movie, he is played by Alan Rickman. He has straight black hair, nearly shoulder-length, and shifty eyes. His movements are fluid and sneaky, rather like a snake.