Each time an Account opt-in a Smart Contract its Local State is allocated in the Account’s state table.
This means that you can have hundreds, thousands or millions Accounts opting-in the Smart Contract, for each one of those the Local State can handle up to 16 variables, stored as key/value pairs.
So, following your example, let’s say that the Local State of your Smart Contract makes use of just one single key/value pair (out of 16), for example a
Balance is a Local variable, its value will be different from account to account, but is still going to be controlled by the same single Smart Contract logic. So if there are 100 accounts opted-in your Smart Contract, you will have 100 different Local states, each one with a specific value for the
Balance key. The Smart Contract can read and write all those Local States.
Hope this clarifies better the Local State concept.