I watched a sort of documentary about him this morning and they focused on his role in Harry Potter.
I have never seen the show as I always thought of it as a kids program.
The books are children's books but for older children. They have some very dark themes, including the deaths of several characters, both adults and children. Snape is the most hateful person in the whole books, short of Voldemort, Harry's arch enemy. Snape was a member of Voldemort's gang when he was younger.
When they announced the casting of the first Harry Potter movie, the casting of Snape is critical. He is Harry's "enemy" throughout his school days. The sarcastic asshole professor he could never please, and who mocked his "golden child status". My 12 year old daughter wanted to know who was playing Snape. I watched Die Hard with her, and her comment about Rickman was "He's PERFECT", and he was.
The role is a thankless one. He is hated throughout. Rickman made himself look ugly, with greasy hair, and a dour demeanor. The loser/bad guy who was always mocked by the "cool kids". And the children are always showing him up. It is not until the very last book/movie, that we find out the truth about Snape. Rickman embodied that role. At once sarcastic, sinister, and cruel, and very bitter.
My personal favourite was Galaxy Quest. The serious actor playing in a cheesy space show.