If something is axiomatic, you can see that it is true without a long proof. It sits at the same level as an axiom: obvious enough, or agreed enough, that arguing it feels like a waste. “It is axiomatic that children need sleep” means we take that as given. In maths, an axiomatic system is one built from named axioms. In ordinary writing the adjective often means “so basic we should not have to say it.” Though actually writers also use it with a little heat, as if the other person should already know: “It is axiomatic that you do not spend money you do not have.” That can sound calmly sure, or it can sound pushy, depending on the room. It is a formal, educated word. You will not hear it much in the playground. Use it when the truth is treated as already settled — not when you are still looking for evidence.