The money in your bank account exists only as a liability of the bank. It is just a number in the bank's database. And each bank has their own database. So transferring money from bank A to bank B means that bank B must agree to take on the liability, in exchange for something else.
Most of the time, the illusion of a global ledger is maintained, but it can break down when the system is under stress (e.g. financial crisis of 2008). Introducing a CBDC would fix this, and would make money work the way we already think it works.