A short hedge is an investing strategy designed to mitigate risk. The word "short" does not refer to the timescale over which the strategy is used. Instead it refers to "shorting" a stock, a strategy in which an investor tries to profit from a stock price falling.
A short hedge is one of a range of techniques known as hedging. The general principle of hedging is that an investor who stands to make a profit if a particular asset or security performs well will take out a smaller investment that will pay out if that asset performs badly, thus reducing the overall losses. If the original investment does pay off, the investor will usually take a small loss on the second investment but still make an overall profit.
The effect of hedging is that both potential gains and potential losses are lessened, thus giving more security to the investor. It might appear at first glance that the same effect could be achieved by simply putting less money into the main investment and not hedging. This isn't the case, as doing this creates the possibility of losing all the investment if things go terribly wrong, whereas hedging means the investor will almost certainly get back some money. Hedging also allows the main investment to be larger, which may allow the investor to negotiate a better buying or selling price.
The short hedge takes advantage of shorting. This involves borrowing a stock from another investor, selling it immediately, then buying back the same stock later to return it to the other investor on an agreed date. If the stock price has fallen in the meantime, the person who borrowed the stock will wind up making a profit. Some of this profit will be eaten up by paying a fee to the other investor for borrowing the stock. This technique works because stock is fungible, meaning that it is completely interchangeable; it doesn't matter that the investor doesn't give back literally the same set of shares as he borrowed.
Using a short hedge is arguably one of the most efficient forms of hedging. This is because, unlike most hedging, it is possible to have both the main investment and the hedge in exactly the same profit. That means that if the investor loses out on the main investment because the price drops, he is guaranteed to make some money back from the shorting. In most other forms of hedging, the two investments are related but different. This means that while a fall in one will normally coincide with a rise in the other, this isn't guaranteed.