Long term fuel trims are what are used by the ECU to keep your car at a stoich air:fuel ratio (14.7:1) while idling and cruising, or under low load conditions. The ECU has a certain range of correction, say +/- 12% to adjust the fuel to keep the car at stoich.
For example the AP allows you to log fuel trims. Basically, you want your fuel trims as close to 0 as possible, meaning the ECU isn't compensating or adjusting either way. If you fuel trim is very positive, like +10%, then the ECU is having to add 10% more fuel than expected to keep a stoich mixture and vice versa for a -10% fuel trim.
On a stock car, you can correct fuel trims by making sure that both your air metering and fuel systems are in good working order and no leaks, such as venting a BOV, etc. In modified cars, with BT,FMIC,Manifold,Meth,Injectors,Fuel Rail,Built Block,Blow Thru MAF, etc, you can use your engine management to adjust the LTFT's, such as in my case when converting to Blow Thru MAF, i had to scale my MAF Table to bring the LTFT's back to a good level.. +0 is best but if its +2 or +3 that isnt bad, when you get up too +12 thats not good.
Hope that explains a little. As far as short term, it's just that...another adjustment that the ECU can make over a very short period, basically on top of the long term fuel, but your ltfts are what you need to keep in order. STFT are just there for minor, quick adjustements.
just a quick explanation..