An inflation swap is an agreement between two counterparties to swap fixed rate payments on a notional principal amount for floating rate payments linked to an inflation index, such as the consumer price index.
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.