Hedging is, in the simplest sense, any strategy designed to offset or reduce the risk of price fluctuations for an asset or investment. When a person or company makes an investment (like when they buy shares of a company's stock), they're betting that the price of that investments will move in a certain direction. As with any bet, there's always the risk of losing if the price moves in the opposite direction; it's this risk that investors use hedging to help offset. Creating a hedge requires the purchase of a second asset with a negative correlation to the first; this can be direct and simple (in the case of a long put to hedge against a long stock position, for example) or indirect and complex (statistical arbitrage between historically correlated pairs, for example).
A basic example of a hedge is buying a futures contract for a commodity, such as oil. For a company that uses oil in its production process, an oil futures contract locks in a price until a given date, protecting the company from the risk that the price will rise even higher by that time. In this case, the company is said to be hedging against rising oil prices. Hedges can, however, fail; for example, if oil prices don't rise by as much as the company expected, it will still have to buy the oil at the agreed-upon price.