How do Ledger Backups get stored?
Using words to back up wallets is a process described in BIP 39.

Basically, the mnemonic is converted into a seed. This seed is then used as the seed to a Heirarchical Deterministic (HD) wallet, as laid out in BIP 32. The seed is used to generate a Master Extended Private Key, from which all other private keys can be generated. The child key generation follows the standard of BIP 44 so it is compatible with other wallets too.

Thus, by backing up your mnemonic words, any time you enter them in a wallet, it can recreate the seed, then the master private key, then all your other keys, so your wallet is back.

References:


http://support.ledgerwallet.com/knowledge_base/topics/how-to-restore-my-backup-without-a-ledger-wallet