I have to admit that I didn't see the source material that this short monologue came from before learning it, though I did know who Azula was and some information about her character. Based on the text alone, I came up with the situation that she, along with some others, were tested on who would be the best one to replace Fire Lord Ozai in the future, even though Azula would be getting the position by default. In this version of the monologue, I imagined that she was talking to a very talented person she was competing against and went on to shove it in their face that she would be the one to win regardless.
I did later see part of the actual situation for the source material and it's definitely different than what my imagination made, so I'll do another version of this monologue in the future with the real/canon circumstances in mind.