Eileen Prince was a pure-blood witch, the wife of the Muggle Tobias Snape, and the mother of Severus Snape. Though her role in the narrative is posthumous and revealed primarily through memories and dialogue, she is a figure of central importance to the plot of Harry Potter and the Half-Blood Prince. Her family name is the source of her son's secret moniker, the “Half-Blood Prince”, and her life provides crucial context for Snape's character, his unhappy childhood, and his complex identity.
Eileen was born into the pure-blood wizarding Prince family. She attended Hogwarts School of Witchcraft and Wizardry, where she was sorted into Slytherin House (Pottermore). During her time at school, she was taught by Potions Master Horace Slughorn, who kept a photograph of her in his collection of favoured students. She distinguished herself not academically, but as the Captain of the Hogwarts Gobstones team.
At some point after leaving Hogwarts, Eileen married a Muggle named Tobias Snape and went to live in the grim, industrial Muggle town of Cokeworth, in a street called Spinner's End. Horace Slughorn expressed disappointment over this union, remarking that she had “let the side down” by marrying a Muggle. Her marriage was deeply unhappy. In a memory Harry Potter witnesses in the Pensieve, she is shown as a “thin, sour-faced” woman being shouted at by her husband, Tobias. The family lived in near-poverty, and the household was evidently filled with conflict. Together, they had one child, Severus Snape. In another of Snape's memories, a young Eileen is seen watching her young son playing with Lily Evans near their home. The date and circumstances of her death are unknown, but it is clear she had passed away before Harry Potter's time at Hogwarts.
As a young girl, Eileen was described as “a skinny, sallow-faced, sour-looking girl.” In adulthood, her appearance reflected her unhappy life; Harry saw her in a memory as a “thin, sour-faced, slutternly woman with long, dank hair and an expression of mingled sadness and resentment.” Her personality appears to have been defined by bitterness and sorrow, likely stemming from her difficult marriage and her fall from the status of a pure-blood witch to a life of squalor in the Muggle world.
While the full extent of her magical talent is unknown, Eileen was a fully qualified witch. Her most notable known skill was her proficiency at Gobstones, a popular wizarding game, evidenced by her role as Captain of the Hogwarts team. She owned a copy of the textbook Advanced Potion-Making, which she passed on to her son, though it is unknown if she herself had any particular talent in Potions.