An interest rate swaption is an option agreement that protects against an increase (for purchasers/borrowers) or decline (for sellers/lenders) in the interest rate swap rate.

By paying a premium in advance (upfront), the client has the right, but not the obligation, to make use of an interest rate swap rate that has been agreed in advance. Depending on its structure, the option can be used on a particular date (European option) or at any time during its term (American option).
If the market rate increases to above the strike price, the client (purchaser/borrower) can benefit from the option in accordance with the agreed conditions. If the swap rate does not exceed the strike price, the option will mature with no value, and instead the client will enter into a swap agreement at the lower market rate. In other words, a purchased swaption is a cap for future swap rates, and a sold swaption is a floor for future swap rates.
Example of interest rate swaption
Swaptions are often used to hedge future borrowing. For instance, these instruments can be used by a real estate company planning the construction of a new property, to be financed through the borrowing facility. 
To ensure that the project is not unprofitable (e.g. due to high interest expenses) the company purchases a 5-year swaption with a strike price of, for example, 7% and maturity within 1 year. If the swap rate after a year exceeds 7%, the company can benefit from the swaption and enter into a 5-year interest rate swap at 7%. However, if the swap rate is lower than 7% after a year, the swaption will mature, and the client will instead enter into an interest rate swap to the lower market rate.