An inflation swap is the linear form of an inflation derivative, and used to transfer inflation risk from one counterparty to another.
Example
An investor takes out a 5-year loan that is repaid at LIBOR+1%. He considers this rate as the sum of real LIBOR plus a credit spread (1%) plus a floating inflation component. He would like to pay real LIBOR, the credit spread, and a fixed rate. So he enters into an inflation swap agreement where for the next 5 years he is paying a fixed rate on his loan's principal while receiving year-on-year inflation on the same amount.