Do I understand Hierarchically Deterministic wallets correctly? Please correct me if I'm wrong.

Basically, any HD Wallet uses a seed phrase, as well as a passphrase/code to generate a master private and public key, right? Once this first key pair has been used, a new pair is created by using the original seed phrase, a passphrase AND the previously determined master private key. Is this correct? Like a tree branching out more and more with every transaction, you gain a new personal address pair.

Basically, I'm trying to understand how my ledger is able to generate an almost infinite amount of new addresses while not requiring any additional input from my side.