EIP-712 is a standard for users to sign structured data that smart contracts can verify. As long as you don't submit the signature to a contract via a transaction, it has no effect. See it as an authorization that costs nothing to produce but is ineffective until sent to a contract that knows how to use it.
Let's take permit as an example. Permit works like approve. The difference is that permit accepts and EIP-712 signature and changes the allowance only if the signature is considered valid. This means that you can sign a permit and anyone else that has your signature could send it to the contract and change your allowance. This is useful because it allows you to pack multiple actions into a single tx.
Without permit, to transfer tokens to a contract:
- send an approve tx to authorize the contract transferring funds from your balance to its balance
- call the contract that will inside its code call a transfer moving tokens from you to the contract
- sign a permit with the same parameters you would have used for an approve
- call the contract with the signature in the parameters, the contract uses the signature to increase your allowance then transfer funds from you to the contract
So only 1 tx for permit while 2 needed for approve.