The seed is all the information that the wallet needs. All addresses are generated from the seed.

BIP-32 describes how addresses are generated from a seed.

You can generate a private key by hashing the seed itself. You can generate another private key by hashing the first private key. You can generate as many private keys as you want by hashing the previous private key. If you start with the same seed, you will always get the same private keys, so the seed is all you ever need. BIP-32 uses that concept.