How do (encrypted) mnemonic phrases work?
A mnemonic phrase or mnemonic seed is a set of typically either 12 or 24 words, which can be used to derive an infinite number of wallets. Often times these phrases are used by cryptocurrency hardware wallets, to be written down on a piece of paper by the user to safely back up the users' funds.
Sometimes these are referred to as backup phrases or seed phrases or 12-word phrase by other wallets or interfaces.
In the Ethereum ecosystem, mnemonic phrases are generally generated following the BIP 32 spec. Popular hardware wallets, like Ledger and TREZOR, follow this spec, same applies to MetaMask. The mnemonic phrase generated by your wallet (usually) consists of 24 words, randomly selected from the BIP 32 English wordlist, some wallets make use of a 12-word mnemonic phrase that are shorter and therefore easier to remember.
Encrypted mnemonic phrases
Many wallets provide an option to encrypt your mnemonic phrase with a password. This is useful as accessing your wallets would require you to have something you have (the mnemonic phrase) plus something you know (the password). Often times this is referred to as 13th/25th word/seed.
However there are some key differences between a typical password and the password that protects your mnemonic phrase. Because the password doesn't encrypt the mnemonic phrase (like the password encrypts your keystore file), there is no "wrong" password. This can be known as a "plausible deniability" passphrase.
Since every password generates a valid seed and will unlock a different account, there is no "wrong" password. It is meant to protect you from the "wrench attack"". It also enables you to create a decoy wallet which has the same mnemonic phrase but uses a different password. If someone forces you to give them access to your wallets, you could provide the decoy password, and keep the real password (with all your funds) a secret.
Mnemonic phrase examples
12-word mnemonic phrase:
jealous expect hundred young unlock disagree major siren surge acoustic machine catalog
24-word mnemonic phrase:
deer swift people fluid team beyond east hello peasant purpose apple pony figure puppy spoon window story run strike scout pave address know stadium
Encrypted mnemonic phrase examples
12-word encrypted mnemonic phrase (where
cryptocurrency is the password):
jealous expect hundred young unlock disagree major siren surge acoustic machine catalog cryptocurrency
24-word encrypted mnemonic phrase (where
encryption is the password):
deer swift people fluid team beyond east hello peasant purpose apple pony figure puppy spoon window story run strike scout pave address know stadium encryption