What does it mean when we say that in blockchain, consensus determines the truth?
Consensus is general or unanimous agreement. In a blockchain system, the computers on the network provide consensus about the validity of a transaction. If there is consensus about the transaction, it is accepted as a part of the blockchain database, and is confirmed as valid. If there is a lack of consensus, the transaction is rejected, and not included in the database. With blockchain, more than one person / device decides about a transaction. Decentralization, combined with consensus, eliminates the need to trust a single person / device. Instead, a network of computers check, and confirm or reject, new data which someone is attempting to add to the database. They prevent incorrect transactions (for example an attempt to spend from a wallet which does not have enough crypto available to pay for the transaction).
The people who own blockchain nodes receive financial benefits, in exchange for providing well functioning computers which provide accurate consensus for transactions. This is a financial incentive, which prevents them from allowing or attempting false transactions in the database.
In addition, with public ledger blockchains, such as bitcoin, anyone can look at the blockchain’s ledger, if they have a computer and an internet connection, and personally get information about transactions on the blockchain. Such openness further eliminates the need to trust a centralized authority.
How is this different from how truth is determined in a central database?
A person using a traditional, centralized database (which can be changed without decentralized consensus), can change the information in that database. This change of the stored data can be done without another person or device checking on the validity of the change. In such a system, belief in the correctness of data is based more on trusting the person who manages the database, though that person might lie or make mistakes. Therefore the data in such a system may be less reliable.