Edge triggering refers to an input that is triggered when the input signal changes from a high value to a low one, or a low value to a high one. An edge triggered input could listen for when a signal crosses a predetermined voltage threshold, or it may utilize a Schmitt trigger (explained below).
An input that activates when the signal changes from below the threshold to above it is said to trigger on the rising edge of the signal. One that activates upon a change from above the threshold to below it is said to trigger on the falling edge.
A Schmitt trigger is a special kind of trigger circuit designed to prevent rapid switching when a signal holds near the threshold. For example, if a traditional trigger circuit had a threshold at 0V, and it was fed a constant signal of 0V, ambeint noise in the signal would cause it to pass back and forth across the threshold very rapidly, with presumably undesired effects. A Schmitt trigger solves this problem by moving the threshold when it is triggered. Upon a rising edge, the threshold is decreased so the signal doesn’t immediately fall below it again. Similarly, upon a falling edge, the threshold is increased.
A chart illustrating rising and falling edges for regular and Schmitt triggers is below.