Maximal exit pupil diameter is an important information when you are buying an optical product, that will be in use in the twilight. This information tells us, at what diameter the light comes through the optical product, where it then enters the pupil in the human eyes.
The exit pupil diameter can be easily calculated from the magnification and objective diameter of the optical product. The objective lens diameter has to be divided by magnification, and then you get the exit pupil diameter.
For example; an 8x56 binoculars have an exit pupil diameter of 7 millimeters, and 10x42 binoculars have an exit pupil diameter of 4.2 millimeters (56:8=7; 42:10=4,2).
The pupil diameter in the human eye changes in different lighting conditions from 3 to 8 millimeters. On a bright sunny day, the pupil is very small, because of the excess light. In the twilight, the pupil gets bigger so more light can pass through to the retina.
So if you have a 10x42 binocular, which has a 4.2-millimeter big exit pupil diameter, you won't have as a bright picture like with the 8x56 binocular. This is because the pupil of the human eye will be at its maximum dimension of 8 millimeters, but the light will come through the binoculars only in 4.2 millimeters.
It is a little bit different with variable magnification optical products. There the exit pupil diameter isn't always the same dimension, but it changes simultaneously with the magnification. For example; if we have a rifle scope with a magnification of 3-12 and an objective diameter of 56 millimeters, at maximum magnification we have an exit pupil diameter of 4,7 millimeters. At the smallest magnification on the other side, the exit pupil diameter should be 18.7 millimeters, but because such a big diameter would not have any advantage (because the human eye pupil is maximal 8 millimeters big), the manufacturers install an optical insert which doesn't let the exit pupil diameter grow too big at small magnifications. This is also our maximum exit pupil diameter. If we take the magnification of 7 times, the exit pupil diameter is 8 millimeters, what would be perfect for the brightest picture through this particular rifle scope.