A hedge is an investment or trade designed to reduce your existing exposure to risk. The process of reducing risk via investments is called 'hedging'.
Most hedges take the form of a position that offsets one or more positions you have open, like a futures contract offering to sell stock that you have bought. Hedging can come in many forms, however, like buying an asset that tends to move inversely with the asset you are holding.
A hedge that removes all risk from a position – except the cost of the hedge itself – is referred to as a perfect hedge, but most traders will only hedge against part of their position.