"Understanding" is clearly linked to compression. Taking observations and coming up with a more compact representation that explains them, analogous to coming up with a compact set of axioms that generate facts, or a small Turing machine or short program that generates a list of strings.

Intelligence is a broader concept but definitely involves understanding how a system/envoronment works and making predictions about its unfolding, especially actionable ones that allow you to steer that state towards some goal states.

These are not new.