Sharing their secret affinity for magic, Severus Snape and Lily Evans were best friends growing up. When the two characters arrive at Hogwarts, the Sorting Hat places Severus in Slytherin House and Lily Evans in the rival house, Gryffindor. Lily and Severus' relationship becomes strained as the two drift apart; Severus joins an unsavory group of Slytherin boys, and Lily is romantically pursued by James Potter, a boy who frequently bullied Severus.
The breaking point in their relationship occurs when Severus lashes out at Lily following a scene in which James Potter and his friends humiliated him. Severus calls Lily a "mudblood," a nasty name for magic people with muggle heritage. Even though Severus tries to gain Lily's forgiveness later, she will have nothing to do with him. She marries James Potter after seventh year at Hogwarts.
Snape does not get the chance to ever marry Lily Evans for many reasons. One of the main ones being that she is in love with James Potter, whom Snape hates quite a bit. James and Lily were dating while they were in school, which made things difficult for Snape. He was also quite afraid and shy, making it very hard for him to find the courage to ask her out.