Harry Potter and the Half-Blood Prince is the film most loved by audiences, because it laid the foundation for Harry to search for Voldemort’s Horcruxes as well as a series of other changes.
Later, the film revealed to the audience the identity of the Half-Blood Prince as Severus Snape.
Although Snape’s recognition that he was the Half-Blood Prince shocked Harry Potter and forced him to give up the book, the knowledge in it helped him a lot in his studies, as well as his later journey against Voldemort.
Lily is the Half-Blood Prince?
From the fact that Lily’s name is mentioned almost every time Harry uses the Potions book, plus the fact that Hermione has many times hypothesized that the Half-Blood Prince might be a girl, it is very likely that the owner of the book is a girl.
Of course there is no confirmation that Lily is the Half-Blood Prince, but the book is important `evidence` of the friendship between Lily and Snape.
On the other hand, this doesn’t mean that Snape isn’t good.
So in general, this book has many layers of meaning, as it can be considered a `memento` left by Lily’s mother to Harry, a treasure of the little student that Slughorn loves so much, and also
Source: Screen Rant