During the Harry Potter series, Harry stumbles across a book, with the contents of a journal. Signed within, was " This book is the property of The Half Blood Prince". Harry reads the journal and finds useful spells and information that saves him many of times during this part of the series. Throughout it, Harry is attempting to discover who this smart and helpful owner of this book is. By the end of the book and movie, it is discovered that SEVERUS is indeed the true Half Blood Prince. This is discovered during a battle between Harry and Severus, when Harry uses Severus' own spell that Harry read in the book, in Severus.
Below is a video of when Severus confesses that he is the Half Blood Prince.
The reason behind this name, is the apparent half blood wizard Snape truly is.
"Half-Blood" in relation to Religion
This idea of the half blood savior is significant as the situation regarding parents that Snape has, is similar to the one told in the bible of Jesus Christ. Although Jesus' mother, Mary, was of human form and his father was the almighty and powerful God, the role of Snape's parents is reversed. Snape's mother was Eileen Prince, and his father's name was Tobias Snape. His mother was the witch and his father was the muggle. Eileen held all the powers and aided in the major creation of the wizard Severus became. It is significant that the author, J.K. Rowling, created great awareness of Snape being a "half-blood prince". Thus, further adding the already apparent suggestion of Snape's relation to the savior, as he already possess the qualities of a savior and now, Rowling relates his family life to Jesus.