Entropy, mnemonics, and the BIP-39 standard
A private key is, at bottom, a very large random number, 256 bits for the elliptic curve most chains use. That number is unreadable and unmemorable, so BIP-39 defines a way to encode a source of randomness (entropy) as a sequence of common words drawn from a fixed 2048-word list. 128 bits of entropy becomes a 12-word phrase, 256 bits becomes 24 words. Each word encodes roughly 11 bits, plus a checksum built in at the end so a wallet can detect a typo or a wrong word.
The mnemonic is not the private key itself. It is a human-friendly encoding of the entropy that seeds a deterministic process. Feed the same 12 or 24 words (plus an optional passphrase) through the standardized PBKDF2 function BIP-39 defines, and you get a 512-bit seed. That seed is the actual root of everything the wallet can produce. This is also why word order matters completely: shuffle two words and you get an entirely different, unrelated seed.