Consensus is the way that the XRP Ledger solves the ‘double spend’ problem without proof of work. We can all agree which transactions are valid or invalid, the basic rules of a transaction are simple. Transactions need to be properly signed or authorized, you can’t send money that you don’t have, etc. The problem is when Jim has 1 XRP or 1 Bitcoin or 1 Dollar, we want Jim to be able to send that to Julie if that’s what he wants to do or we want him to be able to send it to Bobby if that’s what he wants to do. But if Jim can do both options then we have a huge problem. Even though by itself both transactions are valid, there needs to be consensus on the order of transactions, so that it can be agreed upon that one is valid and the other can’t be valid. Historically, the bank has played the role of approver of transactions. For example, if I write a check, my bank will either say that I have the funds or I don’t. And if I write 2 checks for $100 and I only have $100 total in my account, they will process 1 first and the other will be declined. In a decentralized system, by design, there is no central authority so another method is needed to reach an agreement. Bitcoin uses the Proof of Work, Ripple does not.