Recent models of binoculars can be so powerful that they are better described as two small telescopes, always pointing in the same direction, with the two oculars arranged so that it is possible to look through them using both eyes. Most binoculars have a mechanism for changing the distance between the oculars, to adapt to different observers. Also, a dioptre adjustment is often employed on one (usually the right) to make up for the differences in the focussing of the two eyes.
The conventional way to describe binoculars is to use two numbers separated by "x", for example "7x49". The first number is the magnifying power, the second the diameter of the objective lens, the one further from the eye, in millimeters.
Binoculars range from small 3x10 models, often used in theaters, to average 7x50 or 10x50 for amateur astronomy use, to big 20x80 or even 20x140 "galaxy" models. The biggest models are actually powerful telescopes, and their high magnifying power means that a static mounting is necessary for their use, since otherwise natural small hand movements would be amplified too much. A practical limit on hand-held binoculars can be put at 9x or 10x.
Of particular interest, for astronomic use, is the ratio between magnifying power and objective lens diameter. Due to the way binoculars are made, the resulting ratio is the diameter of the final image on the oculars. For example, a 10x50 binocular produces a 5 mm image. For maximum efficiency, this image should match the eye's pupil diameter, that in dark environments grows to about 7mm.
This ratio is also a measure of the brightness of the image. Thus, 10x50 and 8x40 binoculars have the same brightness, although the latter has a smaller image.
A smaller image would use only partially the observer's eye, while a larger image would be impossible to see in a single glance.
Because of this, binoculars with a magnifying power like 7x50 or 10x70 (close or at the 7 mm ratio) are the best choices for their diameter, giving so to speak the best "bang for the buck".
Binoculars have the advantage over telescopes and monoculars of the same diameter of using both eyes at the same time, thus giving a better experience to the observer, partly due to the stereoscopic image.