Static limbs do not bend at the recurve portion. This forces the limbs to bend closer to the riser, which decreases string angle and makes the bow smoother (less stacking) and somewhat faster and may be somewhat quieter. This also allows for a shorter bow behaving more like a longer one in terms of smoothness.
Non-static limbs bend to the nock. In other words, the recurve part straightens as the bow is drawn. This can cause stacking but does not always do so. It does increase the string angle, however.
Both work fine if constructed well. Hope this helps.