A non-standardized contract between two parties to buy or sell an asset at a specified future time at a price agreed on at the time of conclusion of the contract. This is a derivative.
It is similar to a futures contract with the exception of being standardized. The futures market has exchanges which establish standard terms for each contract. With a forward, the two parties decide on the amount that is applied.
Forwards are traded on the over-the-counter (OTC) market. Futures obviously go through exchanges.