Suppose there are 100k shares issued. Some traders decide to naked short 50k. Actual holders of the shares say, "Oh crap. Half the company is for sale - better dump my shares while I still can." So they put up a total of 75k for sale.
Now 50k of the 75k of actual shares need to be purchased by the people selling short, but if you look at the total number available for purchase at that point, you'll see 125k shares for sale - more than were ever issued.
Of course, this same issue can bite the short sellers in a "short squeeze". Suppose we own 60k of the shares in the company. If we see someone selling 50k, we know they are doing a naked short, and we should buy it. When we do, we will own 110% of the company. Obviously, to make things go to 100%, the short sellers need to buy the remaining 10% of the shares from you. You get to pick the price.
* Edited to add - you can see a recent example of a short squeeze in Volkswagen around October 2008: http://www.reuters.com/article/idUSTRE49R3I920081028