Evoked Potentials (EP) are electrical responses produced in the nervous system by stimulation of some kind. Clinical neurophysiology is most commonly concerned with stimulation of one of the senses - usually vision, hearing or the sensory nerves in the limbs. A single EP resulting from one stimulus is normally quite small and difficult or impossible to distinguish from the background EEG activity.
If the evoked responses, to many stimuli, rather than just one, are collected and averaged the signal emerges clearly. All the electrical activity not directly related to the stimulus is averaged out and disappears from the recording, allowing the response caused by the stimulus itself to be seen quite easily.