In the blockchain, transactions are part of blocks. Each block refers to a previous block adding to previous proofs-of-work, which forms a chain of blocks. Once a chain is formed, it confirms all previous bitcoin transactions and secures the network. This not only helps solve the double-spending problem, but it opens the doors for a myriad of powerful applications.
Banks for many years have also used ledgers to track and manage financial transactions, however, bank ledgers are historically private and closed. The general public cannot view them, doesnt have access to them, and they are centrally managed by the financial institutions; essentially they are permissioned ledgers where banks oversee them with impunity.
The difference between the two is that the blockchain is completely decentralized and open source. This means that people do not have to rely on or trust the central bank to keep track of the transactions.