The exact details of payment systems vary from country-to-country. The payments systems handle the multitude of transactions.
But if we are willing to simplify away the complexity of payment processing, private banks do have an account at the central bank, and transfers between banks are effectively transfers between those accounts. The central bank is a bank, and this is exactly how banks will handle transfers between its own customers.
These balances are generically referred to as settlement balances, but in a country with reserve requirements (like the United States), these will be refered to as bank reserves. It is fairly easy to find discussions of bank reserve operations on the internet.