" ...I'm going to find out more about Eileen Prince if I can. ...And the first place I'll look ... is records of old Potions awards!"
-- Hermione Granger (HBP25)
Eileen Prince Snape was Severus Snape’s mother, a witch who appeared to be unhappily married to a Muggle (HBP13).
A picture of Eileen as a fifteen-year old is described as skinny and “simultaneously cross and sullen, with heavy brows and a long, pallid face” (HBP25). She was the captain of the Hogwarts Gobstones Team (HBP25).
Her husband was Tobias Snape, a Muggle (HBP30), and they lived in Spinner’s End, a run-down part of the city of Cokeworth (Pm). During Occlumency lessons, Harry accidentally caught a glimpse of Severus’s family life: Tobias yelling at a “cowering” Eileen, while young Severus cried over in a corner (OP26). Among Snape’s memories in the Pensieve was one of Eileen waiting with him on the platform for the Hogwarts Express, a “thin, sallow-faced, sour-looking woman who greatly resembled him” (DH33).
Both of Severus’s parents seem to have been neglectful. On the playground with Lily and Petunia, Snape wore mis-matched clothes that seem to be too large for him, and he was in no hurry to go home (DH33). When Lily asked Severus whether his father liked magic, he replied “He doesn’t like anything, much.”
Eileen was married to Tobias Snape. They had a son, Severus.
One can only conclude that Eileen's half-magical marriage was a failure, and this unfortunately made her son's homelife miserable. Yet we know that Snape still loved his mother, using her maiden name to form a clever nickname and persona for himself as "The Half-Blood Prince," a boy-genius who revised a copy of Advanced Potion-Making (HBP9, HBP28). Hermione thought some of the notations in the book seemed to be written in a woman's hand, so perhaps the book originally belonged to Eileen (HBP10). However, Harry felt the "Half-Blood Prince" had to be a "bloke" like himself, and he was right. Perhaps Snape's handwriting simply resembled his mother's, since he was so much like her in other ways.