How does a few wallet backup words remember everything?

Places like Bitpay (and others) claim that not even they can access your bitcoins because nothing is stored anywhere online. So, you download the app, get a backup 10 or 12 words and then you can import private keys and store it in your bitpay app bitcoin wallet(s) on the device. They say these wallets are stored on the device and never on some server/cloud.

One day this device gets lost, you get a new device and restore everything with the 10 or 12 words and whalla, all your account details and wallets and bitcoins are back.

How is it possible that 10 words, that were given to you before the time, when you opened the account, can remember everything you added afterwards, all your private keys and all your account details, bitcoin balances and everything else that you entered afterwards, if none of those details are stored somewhere online?