1. What does it mean when we say that in blockchain, consensus determine the truth?
In blockchain in order for the network to function reliably and efficiently it was designed so that the entire network must agree on a consensus on the status of the ledger. The consensus mechanism is a secure way to ensure that all the transactions occurring on the network are genuine and all participants must agree. The participants of the blockchain are financially incentivized to play by the set rules.
2. How is this different from how truth is determined in a central database?
Consensus in blockchain removes trust and is achieved through financial incentives. In a centralized system, an administrator has the authority to maintain and update the database. The task of making any changes is performed by a central authority who is the sole person or persons in charge of maintaining genuine records. This authority is highly unverifiable and would have to be trusted in their role.