A swap is an exchange of financial obligations under a formal agreement between two parties. It is mostly used in respect of interest rates and foreign exchange rates. I will use interest rate swaps as an example.
Let's say you have a loan from a bank where you pay interest at a margin above base rate, but you would prefer to have a fixed rate of interest rather than take the risk of Base rate fluctuating. One way of mitigating this risk is to find another party who has a similar but opposite desire - i.e. they have a fixed interest rate bank loan in the same amount and term but they want a floating rate. You and the other party therefore agree to 'swap' obligations so that you end up with a fixed rate and he ends up with a floating rate. That's all very well in theory, but how likely are you to find someone who has a bank loan in the same amount and term as yours, who wants a floating rate of interest? Not very. Therefore, you approach a financial intermediary (e.g. a bank) who fulfils the role of the other party you are looking for. The swap is separate from the underlying loan, but normally the amount and term of the swap matches the amount of the underlying loan to give you what's called a 'fully hedged' position. On each occasion when interest is due on your loan, you and the intermediary pay each other the interest on the swap - in your case, you pay him fixed interest on the amount of the swap and he pays you whatever the floating interest is on the amount of the swap. In pratice, you don't both make payments, but you net them out so that one party pays the other the net difference. The only time payments are not made is is the fixed and floating rates were the same for the period in question. You still have to pay the original lender interest on the underlying loan at the original floating rate, but if the fixed rate is lower then you receive the diference from the swap counterparty, and if the floating rate is lower then you have to pay the dif