The eye pupil refers to the iris pupil - it is a circular hole, located in the iris center. The iris pupil can regulate light entering the retina.
The autonomic nervous system controls the pupillary reactions. If the light diminishes, the iris dilator muscle causes the iris pupil to dilate - this allows more light entering the retina. If the light becomes bright, the iris sphincter muscle causes the iris pupil to constrict - this can limit light reaching the retina.
Sometimes the iris pupil does not react properly, due to cranial nerve or muscle problems. The common diseases are anisocoria, pupillary paralysis, various pupillary defects. Anisocoria means that, the two pupil sizes are different. Pupillary paralysis often makes the iris pupil unable to constrict.