Mnemonic is a word describing a system that helps you to remember something. There are many mnemonic systems, including rhyming schemes, abbreviations, songs, and others which all have the goal of making it easier to remember some longer and more complex thing.
In the case of cryptocurrencies, some wallets include a mnemonic phrase as part of the seed generation in order to make it easier for you to remember your private key. This mnemonic seed phrase is an easier to remember string of words, rather than the usual alphanumeric string used as a private key.
This mnemonic phrase can also be used as a recovery seed in some cases, so it is very important that you either remember it or write it down and don’t lose it, because otherwise you could lose access to your cryptocurrencies at some time in the future. Try not to keep it anywhere it can be stolen or destroyed, and also try to keep it separate from other information regarding your cryptocurrency wallet.