I see it as just an ability she has

I've always thought it was either natural or accidental.

I think maybe she might have been trying to get more powerful by being more aggressive while seeming calm, but it changed colors by accident. So I think it was intentional but accidental, if that makes sense.

Makes sense. Like she had one goal but achieved something else in the process. Like a bonus.

Didn't the creators say something about it being a reflection of her personality? So it'd be natural or accidental.

They did, I think. Or that was a common rumor or something.

It's my head-canon that Zuko and Azula grew up with tales about Sozin and how he managed to produce blue fire on the day of the comet. So in order to get Ozai's attention, Zuko tries his best to get the blue fire and Azula, not wanting to be outcompeted, does the same but only she is able to finally do it. Something along those lines that would further cause the rift we see between them in the original series.

That's a really neat theory.

I'm gonna copy and paste from a Yahoo Answer I read:

"First, she is a child prodigy, which means she has mastered the art of firebending completely, and makes her fire hotter than normal. Yes, it may mean she is more powerful because she was a PRODIGY. In real life, very hot fire is in fact blue. Plus, if you pull apart Azula's name, you get Azul, which translates to "blue". Plus, learning from the last episode, she has an internal balance that is completely out of whack, which may affect her firebending."

If fire is really really hot, then it is blue, correct? So her fire being blue just shows her power.

^ I believe that's how it is.