Why is an action potential an all or nothing process?

An action potential is the signal neurons use to communicate with each other. It is caused by the rapid opening of sodium channels and influx of sodium ions. Because at rest the inside of the neuron is negative, positive sodium ions rush into the cell when the sodium channels open. The opening of sodium channels is caused by a stimulus. When enough sodium ions have entered the neuron, a threshold is reached and this causes far more sodium channels to open, resulting in a much larger sodium ion influx. This is the 'trigger' which sets off an action potential. 

The reason why an action potential is an all or nothing process is because unless this trigger is reached, an action potential will not happen. A small stimulus may cause some sodium channels to open, but it may not be enough to reach the threshold, so no action potential will take place. However, if there are several small stimuli in quick succession this may be enough to reach the threshold and produce an action potential.