Hi, The short term trim is an adjustment to the injector pulse width that tried to react almost instantly to a difference between actual Lambda and Aim Lambda. The long term trim reacts over a much longer time.
For example if the engine was always a little bit too rich on average the short term trim would spend more time triming fuel out (lowering pulse widths) with the ocasional lean times where the ECU increases the pulse width but it is the average time which is important. With most of the time spent taking fuel out the long term trim would slowly start to take fuel out to more or less offset the Lambda control to always be taking a little fuel out and let the short term trim worry about the instantaneous Lambda errors.