In finance, a hedge is an investment that is taken out specifically to reduce or cancel out the risk in another investment. Usually they come in 2 flavors Options and Futures.
Take a farmer (the earliest form of hedging): you expect to grow wheat and expect the price to be 800 per quintal with a cost of 600/- for you. Now if the price of wheat after 6 months is 700/- , your profit reduces by half, without any fault of yours. Similarly increase of price to 900 will increase your profit by a third. So:
1) So you take the price fluctuation as an act of god and live with it (or maybe even commit suicide).
2) You fix the price with the grain merchant by having a futures contract with him. So irrespective of the market prices at the time of harvest you will be paid 790/- per quintal. You lose 10/- but it removes the uncertainty from the mind of the farmer. On the other hand the merchant earns an extra 10/- plus he is assured of the grain even if the prices go sky high. So for a small fee, all the uncertainty is transferred to a second party.
3) The farmer might not want to lose on the windfall he might make if the price rises. So he instead of the derivative, he buys an insurance policy (the option contract). This contract gives the farmer a legal option to sell at 800. For the merchant to bite this bullet he pays him a sum upfront say 15/- (which is non returnable). So if the price falls, he sell it to the merchant at 800/- and is shielded from any losses. However if the price of the wheat rises above 815/- he actually makes a profit by selling it to the open market.
Point 2 is an example of futures, while point 3 is an example of options. Together these 2 constitute the derivatives market which is used for hedging your stocks.