Why was the Half-Blood Prince important?

Answer 1

SPOILER WARNING!

The Half Blood Prince (aka Snape) wrote notes in his potions book. When Harry wound up with it, Harry used the notes and became better at potions than anyone else in the class. The notes weren't just for potions though. They also had spells and other stuff, including the "Sectumsempra" curse that slashes Malfoy badly in the sixth, and cuts off George's ear in the seventh.

Answer 2

It was significant because Harry found the half blood prince's book (Snape's book) that had improved methods for making potions. Because of the book with Snape's notes, he was the only student who made the potion correctly that won him the liquid luck, and he used that to get the true memory from Slughorn about what he told Tom Riddle years ago about Horcruxes.