What's the purpose of key-rotation? What's the purpose of key-rotation?

Does it have any effect on the probability of keys being breached in the first place? Does it refer to avoiding access after a breach to all past data, all future data, both or none?
As @SEJPM notes, the primary purpose of rotating encryption keys is not to decrease the probability of a key being broken, but to reduce the amount of content encrypted with that key so that the amount of material leaked by a single key compromise is less.

However, for signing keys there is a concrete reason: say it takes $X$ months of computation (expected value given your threat model) to crack a key, and you rotate your signing key every $X-1$ months and revoke the old one, then by the time an attacker has cracked the key, any new signatures produced by the attacker will either be A) rejected by clients because of key expiry, or B) back-dated to before the key revocation (which should also raise warning in clients).