*What do we mean in a block chain, consensus determines the truth?
A consensus is the majority deciding on the truth. When a transaction comes through in a Block chain, each computer on the network, will decide whether to accept the details , and allow them to register. There is no need to trust any one party, because the transaction has been verified many times, so the truth is confirmed.
*How is this different from how truth is determined in centralised databases?
I am not sure about all professional databases, but the ones I have worked on and what I have researched determin that individuals in different parts of the organisation can input information independently. Therefore, the system requires trust, and is open to the possibility of human error and mendacity. The only recourse would be supervision by the central authority, which is far less reliable and efficient.