Consensus determines the truth in blockchain because it is built on incentive that we all want to make money. All the nodes needs to agree that the transaction is valid before it goes trough, and are rewarded by doing so.
The difference is that unlike a central database where the “leader” makes the decisions, we have a network of party’s deciding what is true and what is not true. For example in Bitcoin, when there is a consensus of the network to make a transaction to go trough. All decisions are being double checked again and again, its not decided by one central database which makes it almost impossible to cheat. So we have trust in the transaction from all the nodes in the network.