Binoculars can be classified as either full-size, mid-size or compact binoculars. The size of the objective lens (aperture) affects how large or small a binocular is. Higher magnification doesn't increase the physical size of the binocular.
Full-size binoculars
(like an 8x42 binocular) offer the greatest light gathering ability and over-all optical performance.
Mid-Size binoculars
with a 30 or 32 mm objective lens are considered mid-size. Some people prefer their slightly smaller size, and a mid-size binocular gathers more light than a compact.
Compact binoculars
(like an 8x25 binocular) are more portable than full-size models and work well during daylight hours, but not during twilight or in deep shadows.
Monoculars are technically half of a binocular, a monocular meant to be looked through with one eye. While not generally used for extended viewing, a monocular comes in handy when you need a quick, closer look. Sizes of monoculars vary: some are as small as a permanent marker!
Watch this video for more information on aperture size: