Mnemonic Phrase is a list of words that store all the information needed to recover the wallet. Wallet software will typically generate a mnemonic phrase and instruct the user to write it down on paper.
If the user's mobile/computer breaks or their hard drive becomes corrupted, they can download the same wallet software again and use the paper backup to get their assets back.
Anybody else who discovers the phrase can steal the tokens, so it must be kept safe like jewels or cash. For example, it must not be typed into any website.