Template:Swap - layman
Swaps come in all shapes and sizes, but at their heart they are an agreement to exchange payment streams. In the simplest example, we could agree for a period of 5 years that I will pay you a fixed interest rate on a notional sum of money, and you will pay me a floating rate on that same sum.
Why would you do that?
Well, imagine you had an income source paying you a floating rate (for example, a corporate bond), but you had a liability requiring you to pay a fixed rate (say your mortgage).
Finding a swap counterparty to swap]] your floating rate income for a fixed rate means you will be able to meet your mortgage obligations from the proceeds of that bond, without having to worry about what happens if floating interest rates fall.