It affects the exit pupil size of the optic. The exit pupil is the size of the image as it enters your eye (point the scope towards a window on a sunny day from inside a dark room and hold your hand behind the scope and that little circle of light projected onto your hand is the exit pupil image).
For daytime use, a larger exit pupil means you can move your head around a little more without getting the black edges when you start to leave the line of sight of the scope. Basically, its easier to get behind the scope without being "perfectly" lined up.
The added benefit to larger exit pupils is in low light as someone else mentioned. If your eyes pupils are dilated, they allow more light to enter, and a larger exit pupil gives you this. If you take a regular scope, say 3-9x40, and look through it on a dark night and crank up the magnification, at a certain point you will see the image begin to get darker. This darkening of the image corresponds to the moment that the size of the exit pupil becomes smaller than the eyes pupil (exit pupil = objective diameter divided by magnification).
Larger exit pupils only let you see more light until the exit pupil itself becomes bigger than your eyes pupil, and at this moment, anything larger is wasted light, since it doesn't enter the eye. the first point (daytime in use) will still apply and is usually how it manifests in your shooting experience.
For your example, on a bight day, a normal persons pupils may be quite small, say 3mm in diameter. Your 50mm scope at 22X has an exit pupil of 2.27mm where the 56mm scope at 22X has an exit pupil of 2.54mm. In both cases the exit pupils are smaller than your eyes pupil, so the 56mm will appear to be slightly brighter. This isn't usually the case, but the high magnification of the scopes kind of puts it into a situation that is normally only encountered during low light conditions.
If the scopes were lower magnification so that both exit pupils were larger than the eye pupil size from the start (say 3-9x40 vs 3-9x50), you would not see a difference in brightness until dusk when your eyes begin to dilate.
Sorry if this post sounds repetitive. I have yet to find a simple concise way to explain this to any of my friends.
