I've been watching the cartoon again recently, and I haven't seen anything that explains why her fire is blue. I understand she can bend lightning. Is the blue flames an extension of this?
As per the cross post from scifi exchange , The reason here flame being blue is attributed to the fact that the blue part of the flame widely believed to be the most hottest part of it, and that blue color was also to highlight the fact that Azula was a most skilled fire bender and in terms of raw power her power is second compared to that of Fire lord Ozai.
I personally think that she was the primary antagonist of the second season and to showcase her power and make her a formidable match to Aang they made her flames blue to highlight her proficiency and prowess are much higher than Zuko's who was quite weak in his encounters with Aang in the first season.
The excerpt from the Avatar wiki also confirm the cross post's highlighted points
Azula's characteristic blue flames symbolized the power she possessed and constantly sought to increase. Her apathy also accounted for her ability to create and direct lightning, the "cold-blooded fire". According to Iroh, the skill required complete control of all emotion, which would not prove difficult for Azula with her one-track mentality. Because of these skills, she was also an excellent tactician, regularly displaying cunning, perception, and resourcefulness that allowed her to take advantage of almost any situation. She possessed good self-control, facing down Long Feng and deceiving him when held captive and could lie with a straight face and no physical reactions.