The Book of the Beast is an ancient tome and the most unholy grimoire where witches and warlocks inscribe their names in to devote themselves to the Dark Lord and the Path of Night.
On the night of a witch or warlock's sixteenth birthday, he or she has to pledge allegiance to the Dark Lord in a ceremony known as a dark baptism. There, the witch or warlock has to sign their name in the Book of the Beast with their own blood with a bone quill. Once this has occurred, the witch or warlock is forever bound in servitude to the Dark Lord.
The Book of the Beast is not always called upon during a witch or warlock's dark baptism. Sabrina Spellman was able to sign her name in the book even after she initially refused to do so on her sixteenth birthday. However, it should be noted that the Dark Lord specifically sent Madame Satan to manipulate Sabrina into choosing the Path of Night, so using the Book of the Beast outside of dark baptisms might be rare.
The Book of the Beast was present at the dark baptism of Sabrina Spellman. As Faustus Blackwood guided Sabrina into signing her name in the book, she realized that she did not want to give up her mortal life and follow the Path of Night. Subsequently, Sabrina decided to flee from her dark baptism.
Father Blackwood revealed that Sabrina's father, Edward Spellman, had signed his daughter's name in the Book of the Beast as part of an agreement so that he could marry a mortal woman.