Exopthalmia, or "popeye", describes the protrusion of one or both of the fish's eyes. It is a sypmtom, rather than an illness itself, and has a few possible underlying causes.
Male betta with bilateral (both sides) exopthalmia, or "popeye". Note also the whitish/cloudy slime visible on the right eye. This is indicative of a bacterial infection (specifically, Columnaris). This fish was successfully treated with antibiotics, making a full recovery.
Determining the underlying cause of popeye is important and will influence the treatment course followed.