The two big lenses at the front of the binoculars are the “objective lenses”, also called the “aperture” of the binoculars. The size of these lenses are very important and that information is printed on every single pair of binoculars, e.g. 8×20, or 10×40 or 12×50. The second number (20, 40, 50) is the diameter of the objective lens (in millimeters); the first number (8x, 10x, 12x) is the magnification or power of the instrument.
Bigger lenses gather more light, so the image is clearer and brighter. The size of these lenses are not that crucial in bright daylight, but in fading or dim, light or when focusing on something in the shade of a tree, bigger lenses give a brighter image than smaller objective lenses. The 56 mm. , 63 mm. and giant binoculars are particularly suited for low light conditions.
However, bigger lenses also means more weight overall. Pocket binoculars have certain advantages for being so compact, light and easy to travel with, but does have a disadvantage as far as light gathering is concerned, since their apertures are 25 mm at the most. In the end the the prospective buyer will have to make some choices and eventually settle for a compromise best suited for his purpose.