#1. The consensus (in agreement) is achieved via participants (nodes) looking at a new transaction and then comparing it to the blocks already recorded. This is a method to validate whether this transaction is possible (true) or not possible (false) Example: if I create a transaction and I claim that I have 10 bitcoin and I want to pay or send these bitcoin to Ivan Tech. Then network nodes will look at this new transaction and then look into previous blocks. The nodes would find that I have never accumulated 10 bitcoin therefore the new transaction would be (false) this transaction would be ignored as not true and Ivan Tech would not receive the value of 10 bitcoin. This transaction would be ignored and not written into a new block. If however, I had accumulated 10 bitcoin the nodes would agree that this transaction was true and the new transaction would be written into the next block and it would be recorded that Ivan Tech received a value of 10 bitcoin from me.
#2. A central database is generally controlled by one entity. This entity has the ability to manipulate the database to show what ever value is desired. It is extremely easy to lie through a database when you are the one controlling it. Transactions, amounts and dates can all be changed and manipulated at any time.