A zero-knowledge password proof is a way for one party to prove to another the knowledge of a password, without revealing anything else about the password.
Such a protocol prevents an attacker (eavesdropper or man in the middle) from brute-forcing the password offline even if they capture the whole exchange, so insecure passwords become much less of a risk as long as the verifier rate-limits login attempts on its end.
Some of these also have the property that a malicious verifier can't fake a success unless it already knows the password, thus making password phishing pretty much pointless: the only thing a phisher can verify is whether the user uses some predetermined password, and if not, the user is immediately made aware that the site expected another password.