An implied volatility is the volatility implied by the market price of an option based on the Black Scholes option pricing model. An interest rate swaption volatility surface is a four dimensional plot of the implied volatility of a swaption as a function of strike and expiry and tenor. The term structures of implied volatilities which provide indications of the market’s near and long term uncertainty about future short and long term swap rates. A crucial property of the implied volatility surface is the absence of arbitrage.

https://ia801404.us.archive.org/26/items/ir-swn-vol-6/IrSwnVol-6.pdf