There are many different explanations available on the internet regarding exit pupil, and they can sometimes be confusing. The simple explanation is that exit pupil is the width of the beam of light coming through an optical system. Still confused? Don't worry, it's quite complicated.
Optical systems such as binoculars, spotting scopes, and rifle scopes utilize several lenses to magnify the image you see when looking through the eyepiece. Because of this, the light is bent into a cone that enters the pupil of your eye at the correct eye relief.
You can observe the exit pupil of an optic by performing a simple experiment. Take a rifle scope or binocular and point it at a bright light. Place a piece of paper behind the optic and you should see how big the exit pupil is; it will appear as a circle of light on the paper.
On binoculars and rifle scopes, the exit pupil can be calculated by dividing the objective lens size by the magnification. For example, a pair of fixed magnification 8x32 binoculars has an exit pupil of 32 divided by eight, or 4mm.
In this example, the cone of light entering the pupil at the correct eye relief is 4mm wide. If your pupil is dialated to 4mm, you'll see a perfect image. If the exit pupil is larger than your pupil dialation, some of the light coming through the optic is wasted, as it falls on your iris and does not enter your eye. If your pupils do not dialate much, and for example only reach 4mm fully dialated, you are not using all of the light gathering capability of your optic.
What this all boils down to is that you should know your maximum pupil dialation, and use that as a guide when looking at optics. If you can't effectively use the entire exit pupil, some value of your optic is lost and you may be better off purchasing an optic with a smaller objective lens.