A hedge is a position established in one market in an attempt to offset exposure to price fluctuations in some opposite position in another market with the goal of minimizing one's exposure to unwanted risk. To put it simple, hedge means that a buy some asset in one market and sell that same asset (or similar assets, gold and silver for example). in a different market, so that regardless of the price change of this asset, I always make money in one market (while losing money in the other market).
For example, an investment banker is currently negotiating a deal to purchase stocks of company A next week. If the deal is successful, the price of stock A will increase drastically, while if the deal fails, then price of stock A will drop. Because I am uncertain whether the deal will be successful or not, I "hedge" my position using the following strategy.
I find a competitor of company A, say B, who is in the same industry. If the deal is successful, then company A will be better off and its share price goes up by 10%. Meanwhile, company B, as a competitor will be worse off because its competitor has just got a big investment, so its price will drop slightly, say by 5%. The reverse it also true, if A went down, then B would go up.
I can create a hedge where I buy some A and buy the same amount of B. Then if the deal was not successful, A will go down, but B will go up, so in fact I don't lose as much as if I only have A. You can see that hedging has provided me with a protection. On the other side, if A went up, B will go down, so I don't make as much as if I only have A. This is the cost of hedging, because reducing risk means less return.
The reason that hedging allows reduction of risk is because you are buying opposite positions, so if one goes up, the other will go down. You will lose some of your profit (or loss) because of this opposite direction movement.
There is one rare case called perfect hedge, where you can remove all risk. For example, in our previous example, if A goes up by 10%, then we find stock C that goes down by the same amount (i.e. also 10%), then by purchasing both stocks, we eliminated all risks. Such cases however are rarely found.

The above example shows how an investor could possibly use stocks that move in opposite directions to hedge. Do you think this is pretty difficult to do in real life?