Azula's blue firebending was meant to symbolize that she was more powerful than Zuko as well as a firebending prodigy, and also to easily distinguish her attacks from his in their fights. She was initially intended to have an arranged marriage during the third season.

How did Azula learn Blue Fire?

After her brother was banished from the capital to look for Aang, Azula spent the next three years relentlessly training her bending, strategy, and combat until she concentrated her skills down into her refined, advanced blue fire technique.

Did Azula always have blue fire?

Blue flames are extremely rare, with only Azula displaying them (even including characters present in The Legend of Korra and the graphic novels.) ... Given that Azula has none, unless it's about herself, the production of blue fire might as well be second nature to her.