In the context of "situations filled with anger or confrontation", the expression "It's On" signifies that the speaker is accepting a challenge, either explicitly presented by someone else or implicitly inferred from a confrontational situation.
For example, in an explicit case, it could involve a direct challenge, like a competition or confrontation, perhaps even a physical fight. Imagine someone challenging the speaker to a game of Tetris: "I'll show you who is king of Tetris!" To which the response might be, "Oh, really? It's on!" This expression conveys the speaker's readiness to accept the challenge.
In an implicit case, the phrase might be triggered by unexpected or confrontational behavior. Picture a scenario where a colleague behaves unexpectedly, and the speaker interprets it as a challenge. The response might be, "Oh. That's how it is now? It's on!," indicating their readiness to engage in whatever situation has arisen.
However, I would like to mention that I have only encountered this expression in fiction.