A mnemonic phrase, or simply mnemonics, is a list of 12 to 24 ordinary words that encodes the master key of a crypto wallet. Anyone who has the words can rebuild the wallet and every private key in it. The term is used interchangeably with seed phrase or recovery phrase, which is explained in full on that page.
Most wallets use the word list and method set out in Bitcoin Improvement Proposal 39; see BIP. Because the phrase is the key, it should be stored offline, as in cold storage, and never typed into a website.