Some of these pictures and descriptions may give away plot details that you might not want to know before watching the film.
Alex is a teenage boy who loves his pet Boa Constrictor named Basil that he keeps in a room-temperature drawer (no heating elements, water, or substrate was needed back in 1971.)
He takes Basil out to let him play on a branch in front of a pornographic poster while he listens to a cassette tape of Beethoven. Alex is also a vicious thug who rapes girls and beats up people for fun. Maybe Kubrick meant us to see his fondness for a snake (and snakes almost always represent something evil in movies) as typical of his abnormal violent behavior. (The snake is not mentioned in the novel.) A comment on IMDB says that Kubrick added the snake because Malcolm McDowell, who plays Alex, was afraid of reptiles.