Like a three legged stand (tripod), binocular performance balances on three legs - 1), 2), 3) as follows :. 
1) Magnification (or Power, how close it makes things appear) and Aperture (or Diameter of Objective Lenses) 
As you will see these numbers imprinted on the binocular itself, Binoculars are specified mainly by a combination of two numbers e.g. 7x40, 7x50 or even 12x42. For example, 7x45 binoculars provide 7-times magnification and have 40mm aperture of objective lenses.
The first number is the size of the binoculars magnification or power itself, which is the degree to which the object being viewed is enlarged. With a 7x40 binocular the image is 7 times larger than what you see with the naked eye. The level of power affects the Brightness of an image, so the lower the power of a binocular, the brighter the image it delivers will be. In general, increasing power will reduce both field of view and eye relief, which are also discussed here. 
For any practical application, magnification usually ranges from 4 to 12. Anything higher than a power of 12x is not desirable for several reasons : 
(i) the amount of light reaches the eyes decreases with increasing power so that the object appears darker at higher magnification, powerful binoculars are useless if the image is dim or fuzzy. 
(ii) the field of view decreases with increasing power; and, most importantly, 
(iii) the higher the power, the more sensitive viewing is to any little movement. As a matter of fact, viewing through a pair of 15x binoculars is an exhausting experience because even your heart beat or breathing with make the image dance around! 
The second number refers to aperture or the diameter of objective lens (the lens furthest from the eye and closest to the object you are looking at) in millimetres. A larger objective lens will take in more light to enhance Resolution and Brightnessalthough there are limits to the amount of light that your eye can receive. It determines the light gathering ability of the instrument, with the greater light gathering ability of a larger lens translating into greater detail and image clarity. This is especially useful in low light conditions and at night. 
Doubling the size of the objective lenses quadruples the light gathering ability of the binocular. For instance, a 7x50 binocular has almost twice the light gathering ability of a 7x40 binocular and four times the light gathering ability of a 7x25 binocular. This might lead you to assume that bigger is better when it comes to the diameter size of the objective lenses, but in reality the size of the lens must be considered along withExit Pupil and intended usage to determine the best binocular for you. 
2) Resolution (sharpness and clarity) 
Resolution is a measurement of the binoculars ability to distinguish fine detail (sharpness and clarity), also referred to definition, is the ability of a binocular to distinguish fine detailand retain clarity Better resolution also provides more intense colour. All else being equal (and it rarely is) a larger Aperture will always deliver more detail to the eye than a smaller Aperture lens regardless of the magnification. 
In fact, actual resolution hinges on variety of factors: the quality of the optical components, light transmission through the binoculars, existing atmospheric conditions (e.g. heat haze), optical and mechanical alignment (called collimation - please don't drop binoculars) and the visual acuity of the user (your eyesight). 
3) Brightness (light transmission) 
Aperture determines the amount of light that the binocular takes in to send to your eye. This in turn largely determines the brightness of the image that you see. The larger Aperture of the objective lens, the greater the brightness and the Resolution(sharpness and clarity, resolving power) of the binocular and of the image seen through the binocular. 
It follows then, that a binocular with a large Aperture of objective lens is best for light conditions such as late afternoons, overcast days and astronomy (star gazing). Though a larger aperture of objective lens means more light enters your eyes, it also means a larger and longer binocular body. If you want to carry around a pair of binoculars, a suitable aperture objective lens is between 20 and 50 mm. 
Brightness can also be improved through the use of optical coating or use a variety and combination of coatings to produce binoculars suited for all situations. All lenses are usually optically coated to reduce scattered light and improve light transmission. One of the most popular coatings on the objective lens is ruby coating, which provides both performance and durability. Optical glass (selected lens and prism) surfaces are coated by magnesium fluoride to reduce light loss and glare due to reflection. Most binoculars are fully multi-coated to further enhance viewing and reduce eye strain. Some binoculars have a special image enhancing, amber, high contrast coatings. 
Main methods of Coating :
Fully Coated: all air to glass surfaces are coated. 
Multi-Coated: One or more surfaces of one or more lenses have been coated with multiple films. 
Fully Multi-Coated: all air-to-glass surfaces have been multi-coated. 
Rubicon tm (Ruby) Coated: Unique to TASCO our Rubicon coating consists of 14 layers of varying colours and composition on the objective lenses. Because of their ability to filter out uncomfortable red light and provide brilliant daylight viewing, this is especially suited to binoculars being used to view objects over water, snow or other bright conditions. 
UVC (ultraviolet) Coated: Removes the glare resulting from excess ultra-violet rays in the atmosphere providing a clearer more vivid image especially in brilliant sunlight. 
Please consider the following other factors when choosing a kind of binoculars. 
1) Field of View (FOV)
The Field of View (FOV) is the width of the area that you can see through the binoculars, which is usually given as degrees or as length at 1000 yards. The FOV is usually printed on the binocular - sometimes as 'x feet at 1000 yards' or sometimes as 'y degrees'. In the latter case 1 degree approximately equals 52 feet at 1000 yards. 
As a general rule the field of view will decrease as Magnification increases. However FOV is dependent on many factors and higher quality binoculars will have a larger FOV than their cheaper counterparts. 
Usually ranges from about 2 to 10 deg, the FOV can also be increased by changing the design and shape of the binoculars lenses and these are known as Wide-Angle Binoculars.
The size of the area that can be seen while looking through a pair of binoculars is referred to as the field of view. The angular field of view is indicated on the outside of the binocular, in degrees. The linear field of view refers to the area that can be observed at 1,000 yards, and is expressed in feet. A larger field of view translates to a larger area seen through the binocular.You can use angular field to calculate the linear field by multiplying the angular field by 52.5. For example, if the angular field of a particular binocular is 8°, then the linear field will be 420 feet, i.e. the product of 8 x 52.5. 
in general. A large field of view is especially desirable in situations where the object viewed is likely to move, or when the user is moving.
2) Exit Pupil
The exit pupil refers to the size of the shaft of light transmitted to the eye. The more light, the better the contrast. You can actually see the exit pupil by holding the eyepiece of the binocular approximately 12 inches from your eye. It is the bright circle of light in the center of the eyepiece. Exit pupil is expressed in millimeters and is normally derived by dividing the power into the objective lens diameter. A 7x50 binocular has an exit pupil of 5mm (50 ÷ 7). 
3) Focusing Range
All binoculars have the ability to be focused for infinity. So a primary point of distinction between binocular models is the minimum focus range. Birders tend to favor models with a short focus range of about 15 feet, but 20 to 25 feet is usually acceptable.
4) Stray Light 
When light entering the binoculars reflects off of interior surfaces, the reflected light eventually exits inside the binoculars in the form of stray light. This unfocused light typically diminishes the image quality of the sight picture. 
5) Twilight Performance 
Using the below formulas gives a basic evaluation of low light performance, however, one must keep in mind that they are mathematical formulas and do not take into effect some of the most critical features in optics; glass quality, number of lenses, precision of manufacturing and coating.
In a word, the Resolution and Brightness of the image you see through a particular binocular or spotting scope is determined by a number of different factors, including the interaction of these factors. Magnification, optical coating and Aperture are just a few of the factors influencing how a binocular performs. 
However, the single most important criterion in performance will always be the quality of the optics. We deliver optical excellence through careful consideration of quality in the glass and lens coatings used, precise manufacturing processes, and excellentQuality Control(Q.C.).