A-process refers to the one of the emotional internal processes or responses of the opponent-process theory. The a-process is in large part responsible for the initial, usually fast and immediate emotional reaction to a stimulus.
There is a peak response to any emotional stimuli which usually occurs rapidly, usually out of shock, but last only as long as the stimuli is present. In a physiological sense the a-process is where the pupils dilate, the heart rate increases, and the adrenaline rushes.
B-Process, however, the other part of opponent-process theory, is after the initial shock, or emotion. A-process and B-process overlap in somewhat of an intermediate area. While a-process is still in effect, b-process starts to rise, ultimately leveling out a-process' initial spike in emotion. A-process ends once the stimulus is terminated, leaves, or ends. Physiological this is where breathing returns to normal, pulse slows back to its normal rate, and heart rate starts to drop.
You can think of the B-process as the "after-reaction".
Once B-process has ended, the body returns to homeostasis and emotions rise back to neutral.