Character Analysis
The Blue Fairy is the Pinocchio universe's Queen Bey—and no, that's not a typo. All she's got to do is put a wand on it and there are no limits to what she can do.
Judge Dredd, Minus the Guns
She doesn't help just anyone, however—you've got to deserve it. Pinocchio only gains his sentience because Geppetto is a swell guy, for example:
THE BLUE FAIRY: Good Geppetto, you have given so much happiness to others. You deserve to have your wish come true.
Ever the stickler, the fairy refuses to complete Pinocchio's transformation into a human until he proves himself to be "brave, truthful, and unselfish." This is another moral test: she wants to know that Pinocchio deserves her gift.
We don't want you to think that she's a harsh judge, however. She comes to the rescue when Pinocchio is captured by the Great Stromboli, for example, giving him further advice to help him on his way. The little guy still trips up, but he ultimately lives up to the Blue Fairy's words and earns his humanity.
P.S.
Before you go on your character analyzing way, we want to take a moment to note the way that the Blue Fairy is animated. While every other human character is depicted in a cartoonish, exaggerated style, she looks photo-realistic by comparison. In fact, animators based the character on Marge Champion, the same woman who modeled for Disney's Snow White.
By juxtaposing this realistic character with a cartoonish world, the filmmakers make the Blue Fairy feel hyper-real. This is an ingenious way of giving her that magical air that sets her apart from mere mortals like Geppetto and Pinocchio.