Information is actually about _reduction_ in entropy. Roughly speaking, entropy measures the amount of uncertainty about some event you might try to predict. Now, if you observe some new fact that has high (mutual) information with the event, it means the new fact has significantly reduced your uncertainty about the outcome of the event. In this sense, entropy measures the maximum amount of information you could possibly learn about the outcome to some uncertain event. An interesting corollary here is that the entropy of an event also puts an upper bound on the amount of information it can convey about _any_ other event.
I think one frequent source of confusion is the difference between "randomness" and "uncertainty" in colloquial versus formal usage. Entropy and randomness in the formal sense don't have a strong connotation that the uncertainty is intrinsic and irreducible. In the colloquial sense, I feel like there's often an implication that the uncertainty can't be avoided.