What did the Half-blood Prince's textbook represent in Harry Potter?

The Half-Blood Prince's textbook plays a huge role in Harry Potter and the Half-Blood Prince as both a plot device and a symbol. The textbook helps Harry succeed in Potions class and teaches him powerful (and dark) magic. For Harry, the textbook represents a possible connection to his parents because he believes that the Half-Blood Prince may have been his father. This connection to his parents makes the textbook all the more precious to Harry. Ironically, Harry feels a strong connection to the Half-Blood Prince without realizing that the Prince is Severus Snape, a man he hates.

The textbook is a temptation for Harry-- a temptation to which he succumbs. The textbook is a source of moral ambiguity: while Hermione condemns Harry's use of the book as cheating, Harry doesn't see it that way. The book is a tool, a source of information, and how Harry uses that information tells the reader a lot about him.