Consensus and the Blockchain
Reaching consensus in the blockchain world simply means that the majority miners (I prefer to think of them as bookkeepers) agree that a particular transaction is accurate. Simple! The difficult part is what rules and procedures (protocols) are there for bookkeepers to follow in order to determine how consensus can be reached. There are of course many different ways.
For blockchain, there are two main protocols, Proof of Work (POW) and Proof of Stake (POS) (there are others). Understanding how these protocols differ, their relative strengths and weakness and how well they are or are not developed on the particular blockchain, is paramount for understanding blockchain technology and for evaluating the long term viability of particular blockchains.
This is early technology and you can spend many hours (as I have done) reading different experts opinions outlining their view of the best form of consensus and the various strategies for dealing with the downside issues of each. Not unsurprisingly there is no consensus among experts as to the best protocol!