The purpose of the blockchain is to create agreement about the ownership of balances.
The problem is that if everybody was creating their own records of transactions they witness, the various records would be in different orders and any conflicting transactions would cause a split in what is considered true. At any point of time it would be very unlikely for any two sets of records to match completely.
Traditional money services solve this by having a trusted entity as the arbitrator and sole source of truth.
Bitcoin solves this differently: Each participant collects all transactions they hear about and repeatedly proposes these packaged as a set of updates. We call these sets of balance updates blocks. Instead of having a sole source of truth, the network holds a lottery to designate one of these blocks as the commonly accepted new status quo of the balances. As each block refers to the previous commonly accepted network state and by its acceptance creates a new commonly accepted network state, the blocks create the eponymic chain of commonly accepted states.
The resulting blockchain contains the record of every transaction ever performed on the Bitcoin network. It also allows any new participant to audit the accuracy of the present status quo of the network. Upon joining, they rebuild the set of balances by applying each block in the right order, and will finally arrive in agreement with the rest of the network.
Relevant: http://bitcoin.stackexchange.com/questions/168/what-is-the-blockchain http://bitcoin.stackexchange.com/questions/12427/can-someone-explain-how-the-bitcoin-blockchain-works https://en.bitcoin.it/wiki/Block_chain
– Charles S – 2015-12-15T18:37:48.280I feel like the problem here is the assumption that bitcoin is more complicated than the financial systems that we already have. It's not -- it's just that most people are well in the dark about many large parts of our financial systems, and aren't even aware that they are in the dark about them. In that case, explaining bitcoin becomes about understanding your audience -- in this case "laymen" -- and what's relevant to them. It's entirely possible that most of what you're trying to explain beyond "it's electronic" money is irrelevant to most of your audience not composed of tech enthusiasts. – John Henry – 2015-12-15T22:07:48.793