It is a common misconception that there are actual objects or chunks of data that are Bitcoin and that your wallet receives. That is actually not the case; your Bitcoin are just values attached to outputs created by previous transactions. Most of these outputs (and the type that your Ledger is designed for) require that the spending transaction contain a signature which signs the spending transaction and corresponds to a public key that was specified in the output that is being spent. That public key has a corresponding private key which your wallet knows about.
When you back up your 24 word mnemonic, what you are actually doing is backing up a number encoded as a string. That number is then later used to generate the private keys for your wallet. The generation method is deterministic, which means that given the same number, your wallet will always generate the exact same private keys. So when you restore your wallet from the 24 word mnemonic, what you are really doing is giving it the number that your previous wallet used to generate the private keys so that the new wallet generates the same private keys. This allows you to then spend the Bitcoin you already have since those transaction outputs can just be retrieved from the blockchain.