TL;DR

Two-factor seed phrases Seed phrases, like all backups, can store any amount of bitcoins. It's a concerning idea to possibly have enough money to purchase the entire building just sitting on a sheet of paper without any protection. For this reason many wallets make it possible to encrypt a seed phrase with a password.

The password can be used to create a two-factor seed phrase where both "something you have" plus "something you know" is required to unlock the bitcoins.

This works by the wallet creating a seed phrase and asking the user for a password. Then both the seed phrase and extra word are required to recover the wallet. Electrum and some other wallets call the passphrase a "seed extension", "extension word" or "13th/25th word". The BIP39 standard defines a way of passphrase-protecting a seed phrase. A similar scheme is also used in the Electrum standard. If a passphrase is not present, an empty string "" is used instead.

Warning: Forgetting this password will result in the bitcoin wallet and any contained money being lost. Do not overestimate your ability to remember passphrases especially when you may not use it very often.

Warning: The seed phrase password should not be confused with the password used to encrypt the wallet file on disk. This is probably why many wallets call it an extension word instead of a password.