re: What is the purpose of swaps?

As already discussed SWAPS are most commonly used to decrease the interest rate repricing mismatch between rate sensitive assets and rate sensitive liabilities, usually for financial institutions. This is hedging interest rate risk on a macro level.

But banks also use SWAPS to create "artificial" fixed or variable rate positions on the transaction level, or micro level.

For example, a bank may want to make a relatively large loan to an important customer and the customer may insist the loan be at a fixed rate for, say, 5 years. The bank may not be able to find fixed rate funding for 5 years to fund the loan and must fund the loan via floating rate deposits.

So, the bank can fund the loan via the variable rate deposits and offset the interest rate risk by buying a variable rate SWAP (in the same amount of the loan) with a 5 year maturity and thereby receive a variable rate income flow offsetting the variable rate expenses associated with funding the loan and paying out on the SWAP a fixed rate with a favorable spread to what it will be receiving on the fixed rate loan thus guaranteeing itself a profitable spread on that transaction over its life while negating the interest rate risk.

All this depends, of course, on the rates on the SWAP being favorable to the rate the bank can charge its borrower on the fixed rate loan.