Short Term: Let's say there is a pharmacudical company that you expect will be given permission to market a new wonder drug next friday, but the world hasn't stumbled onto this fact just yet and so the price of the stock is still low. You might buy that stock today with the expectation that on friday the price will skyrocket, and if it does you will sell it off on monday morning and take your money. It doesn't get much shorter term that than.
Long Term: Let's say that you have been using some companies' products for a couple of years and have come to the conclusion that they are very well managed. When you look carefully at the company you discover that they have decided to increase their internal budget for product research and continue to release new and innovative products for years to come. So you buy the stock with the expectation that its value will continue to grow at a healthy rate so long as they continue their aggressive strategy. You have no intention of selling this stock next monday no matter how much it fluctuates on the daily market because you expect it to double or triple in value in the next several years. So you hold. This is a long term investment.
Another way to think about it is from an economists point of view. For an economist the short term is that period of time in which the variables will remain unchanged. The long term, by contrast, is that period of time in which any or all variables might change. So with a short term investment you are 'betting' that the current situation is very favorable for rapid price increase, like the company that is on the verge of having a new product approved. Long term investments in this case would be made in those companies that you expect will deal with the uncertainty of change very well, will release new products or services that are as yet unknown, and most importantly have management systems in place that allow them to change with a changing world.