Why is Azula's fire blue?
Azula's fire is blue unlike other powerful firebenders who have orange fire. For instance, her uncle Iroh or Fire Lord Sozin, even while under the influence of Sozin's Comet, have orange fire.
One unique feature of Azula's firebending is that she creates blue flames, setting her apart from all other firebenders.
But why is her fire blue?
Also it’s just a tie-in to the character. “Azul” or similar means “blue” in Spanish and many related languages.
The blue part of a flame is widely believed to be the hottest part of the flame.
The regions are also separated by color, the blue region (the innermost part of the flame) being the hottest.
In reality, there are many factors that go into a flame's color, but the color of Azula's firebending is meant to show that it is hotter than the average firebender.
Fire Lord Ozai never used blue fire; presumably he should be more powerful than (or at least on-par with) Azula.
@OrigamiRobot Adding to your answer - from a physics perspective - the color of normal flame is yellow since it does not have enough energy to burn the soot from already burnt particles. It turns to blue if the substance being burnt has energy enough to ionize the soot. So the blue flames for Azula indicate her energy level to ionize rather than burn.