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One way of looking at an interest rate swap is the fixed payer is betting the interest rates will rise, and the variable payer betting they will fall. Its best if you look on page 380 Volume 5 as that is where a swap is initially explained.

Basically without a swap, a company paying a floating rate loan on an asset is exposed to interest rate risk which could result in a negative income spread (return on asset - funding cost)

with an interest rate swap a company can lock in a guaranteed spread on the asset and funding cost regardless of the variable rate it pays.

the example shows a company that pays the floating rate thinks the interest rates will fall (it pays a smaller amount of interest than it receives = gain). swaps can be very beneficial to both companies.

for example currency swaps are used to reduce expense volatility for companies conducting business in other countries because the exchange rate wont cause large or small expenses from period to period.