With traditional methods of payment, you need to trust a third party, such as Visa, Interact, or a bank, or a cheque clearing house to settle your transaction. These trusted entities are "centralized", meaning they keep their own private ledger which stores the transaction's history and balance of each account. They will show the transactions to you, and you must agree that it is correct, or launch a dispute. Only the parties to the transaction ever see it.
With Bitcoin and most other
Ethereum Miner digital currencies, the ledgers are "decentralized", meaning everyone on the network gets a copy, so no one has to trust a third party, such as a bank, because anyone can directly verify the information. This verification process is called "distributed consensus."