This title lets us know right away that we're in for a fun ride. Harry Potter and the Sorcerer's Stone sounds exciting and magical. It reminds us that we're clearly in the fantasy genre (with the idea of sorcerers) and lets us know right away who our hero is (Harry Potter).
There are at least two big things to take away from this title. The first is how it sets the tone for the rest of the Harry Potter series. Each of Rowling's following, bestselling books includes the phrasing Harry Potter and the... [BLANK]. As the series progresses, the BLANKS get tougher and tougher, finishing up in the Deathly Hallows. The Sorcerer's Stone doesn't have quite as mature – we could almost say as dark – an association. In Book 1, Harry's eleven, he's just found out he's a wizard, and he's only beginning to dip his toes into the well of magic. Sure, there's mystery, excitement, and plenty of danger, but there's also lots of joyous discovery about the magical world of Hogwarts and its existence within the Muggle society.
The second thing about the title is, perhaps surprisingly, that this wasn't the original title in the UK. That's right; the first Harry Potter book was actually called Harry Potter and the Philosopher's Stone instead of Sorcerer's Stone. The use of Philosopher in the title doesn't stress magic as much as the revised version does. You could even say the use of Sorcerer reduces the original title's emphasis on education: Philosopher reminds us of the study and quest for (magical) knowledge, while Sorcerer reminds us of magic itself. Others words were also changed to make it sound more American. We don't usually think of British English being that different from American English, but there are tons of little differences. For example, the characters in the Americanized version say "sweater" instead of "jumper."
Critic Philip Nel thinks all this changing of words is a bad idea. He writes, "during its transformation to Harry Potter and the Sorcerer's Stone, Harry Potter and the Philosopher's Stone loses the most in translation. The almost total disappearance of the word 'Mum' is a case in point, illustrating how acts of translation efface cultural specificity" (269). (Source: Philip Nel, "You say 'Jelly,' I say 'Jell-O'? Harry Potter and the Transfiguration of Language," in The Ivory Tower and Harry Potter: Perspectives on a Literary Phenomenon [ed. Lana A. Whited], Columbia, MO: University of Missouri Press, 2002: 261-284.) Check out The Harry Potter Lexicon for a list of all the changes.