Hedging is a way of reducing some or all of the risk involved in holding an investment. A hedge is just a way of insuring an investment against risk.
Consider a simple (perhaps the simplest) case. Much of the risk in holding any particular stock is market risk; i.e. if the market falls sharply, chances are that any particular stock will fall too. So if you own a stock with good prospects but you think the stock market is weak, then you may be interested to hedge your position.
There are many ways of hedging against market risk. The simplest and easy method, is to buy a put option or sell stock futures for the stock you own. (In this case you're buying insurance not only against market risk but against the risk of the specific security as well.)
Investors use this strategy when they are unsure of what the market will do. A perfect hedge reduces your risk to nothing (except for the cost of the hedge).
Other alternative methods using options exist. You can read more on option trading strategies at
http://www.traderji.com/forumdisplay.php?f=29
You could also read more on dynamic hedging strategies at
http://finance.wharton.upenn.edu/~benninga/mma/MiER71.pdf