There are a number of factors that can contribute to short take off landing (STOL) ability.
The Zenith page has some information:
A more "cupped" wing shape generates more lift at a slower speed, enabling a shorter take off. This sacrifices the aircraft's top speed. Note that this limitation can be mitigated by making the wing shape changeable with slats and flaps.
There are other modifications that can be made to a wing shape to favor STOL characteristics. For example, there are a variety of STOL kits that can be added to existing aircraft. These range from wing tips to other airfoil shape changes.
By taking off into a higher speed wind, the takeoff distance is decreased. With a strong enough headwind (and a skilled pilot), a STOL aircraft and appear to take off vertically with little or no runway needed.
Power to Weight Ratio
The more powerful the engine is compared to the weight of the overall aircraft, the less runway is required to achieve takeoff speed.