A seed phrase, also called a recovery phrase or mnemonic, is a list of usually 12 or 24 ordinary words (most often from the English list) that can restore an entire Bitcoin wallet. Lose your phone, and these words bring your coins back. Leak them, and anyone can take your coins.
Where it comes from
The standard, called BIP39, starts with random data: 128 bits for 12 words or 256 bits for 24 (BIP39 also allows 15, 18 and 21 words). A short checksum is added, and the result is split into 11-bit chunks. Each chunk selects one word from a fixed list of 2,048 words. The words are simply a human-friendly way to write down a large random number.
From words to keys
The phrase is turned into a master seed. Using another standard, BIP32 (hierarchical deterministic wallets), the wallet derives a tree of private keys from that seed, along with their public keys and addresses. The derivation is deterministic, so the same words always produce the same keys in any compatible wallet.
The optional passphrase
Many wallets support an extra passphrase, sometimes called the "25th word". It creates a completely different wallet from the same words. It adds protection if someone finds your phrase, but if you forget the passphrase, the funds are gone.
Golden rules
Write it down offline. Paper works. Stamped metal survives fire and flood.
Never type it into a website, chat or email. No legitimate support team will ever ask for it.
No photos or cloud notes. These get synced, hacked and leaked.
Store it safely, and test recovery with a small amount before trusting it with more.
A seed phrase is the heart of self-custody. For larger amounts, some people use multisig so that no single phrase controls everything.