The exit pupil is the size, in millimetres, of the beam of light that leaves the binoculars to enter the eye. It is measured by dividing the size of the objective lens by the magnification.
So, in an 8 x 40 binocular the exit pupil will be 40 mm divided by 8, which is 5 mm.
The importance of this is how it relates to the size of the users pupil.
Maximum Dilation of Human Eye
The pupil in a human eye can vary from about 2 mm when it is very bright, to about 8 or 9 mm when it is very dark. This maximum dilation decreases as we get older, and by the age of 50 the maximum will be about 5mm.
If the exit pupil of the binocular is bigger than the user's pupil, then some of the light will fall on the iris and so is wasted. This will make the image appear dim.
Also, resolution and contrast are adversely affected which results in loss of clarity.
What this means is that the exit pupil of a binocular should be at least 2 mm, but no more than 9 mm.
A human pupil adapted to daylight will normally be between 2 and 3 mm.
Therefore, if you will mainly be using the binoculars or monocular in daylight (or you are over 50), the exit pupil should be somewhere between 3 and 5 mm.
For low light observation, a larger exit pupil would be more suitable (8 or 9 mm).
It should also be noted that it does make a difference if you are going to be using the binoculars when it is difficult to hold them steady (when out on a boat, for example).
In this sort of situation it is better to have an exit pupil greater than the eye pupil. This is because it will be easier to keep the eye pupil centred on the larger exit pupil.