A swap is a financial agreement between two parties where the parties agree to make payments between them based on agreed upon rules. They are primarily used for hedging purposes.
Consider a foreign currency swap. Suppose Company A is a U.S.-based exporter that sells a lot in Thailand, and is thus paid a lot in Thai baht. They want to reduce the risk that the Thai baht will fall in value, so they go to a counterparty and agree to a swap contract whereupon the company will agree to pay the counterparty one million baht every month in exchange for $29,500 (in U.S. currency). That way if the value of the baht declines, the company will not lose money.
Event contracts are legally considered swaps in the United States.