Azula is the daughter of the fire lord, Ozai. And soon, she will be the fire Empress. And the fire nation's tradition dictates that a fire Lord / Empress need to marry. And when a fire Empress marries a man, her husband isnt given any politic power or title, as just serves as a lover for the ruler. In this scenario, the fire nation doesnt necessarily want to invade other kingdoms, and keeps a tense, but stable diplomatic relationship with the Avatar.