Question 1) What does it mean when we say that in blockchain, consensus determines the truth?
Consensus is the method and rules used by the blockchain network to determine the true state of the information held by the ledger. Each individual node on the network must agree that the state of the information held locally is “true”. This is achieved through POW (proof of work) mining, a system where the node proposing a new block must provide the solution to a cryptography problem. Once this problem has been solved, and validated by at least 51% of the other nodes on the network, the block is added to the blockchain. If the new block being proposed has information that has been doctored in some way, validation will fail, and the block rejected. This will result in real term financial loss for the individual node seeking to enter a doctored block.
Question 2) How is this different from how truth is determined in a central database?
In a blockchain, the system is “trust-less”, and transactions verified across the network by independent nodes. This requires no central administration to enforce rules and make decisions regarding provenance and consensus. With a central database, the information is stored locally on data storage systems, and anybody who has access to that data storage system can enter fraudulent information into it. This results in the database being wholly dependent on the honesty of the administrators and organization that service the database, and as a result, the data you entrust to a traditional database then becomes dependent on a high level of “trust” in the administrators.