So I'm going to get all physics-y here, but bear with me.
Thinking in terms of real world physics, some flames will burn blue depending in what it is that you're burning. Certain elements burn blue, other burn green, etc. The reason for this is a little bit long, so I won't write it here. This wouldn't be the case with Azula, since we can almost definitely inffer that she's burning the same thing every other firebender burns: the particles in the air.
So why are her flames blue? Basically, the color of something you see relates to the frequency of the light coming from the object, which is directly proportional to how much eletromagnetic energy that thing is emitting. Basically, red light has low frequency (low energy) and blue light has high frequency (high energy). So if something burns blue, it means it is being burned with lots of energy: AKA it's really fucking hot.
So to summarize: Azula's fire if blue because it burns hotter, which follows along well with the whole "she's a genius" thing.
You can also think of it from an emotional view point: since lightning is called "fire without heart", maybe you could think that Azula's fire being blue relates to that. Since she is quite heartless and mentally deranged, her emotional state is shown via her flames' colors.