Choosing Binoculars: Binoculars come in a wide variety of shapes, sizes and specifications. Because of their large light-gathering capacity and the typical wider spacing of the lenses than the human eye, binocular images are brighter, more detailed and more three-dimensional than normal vision. Since no one particular binocular is perfect for all situations, determining their primary use is one of the most important factors in choosing the right one for your needs. 7x50, 10x50, 8x60: what do they mean?
The first number (7 in 7x50) is the magnification. A 7x binocular makes objects seem 7 times closer. The second number (50 in 7x50) is the diameter of the binocular's objective lens in millimeters. The objective is the lens that you point at the object you're trying to see. Bigger objectives gather more light, so a 7x50 binocular shows you more in dim light than a 7x35. The exit pupil is the ratio of lens diameter and magnification. In case of 7x35 it is 5 mm, in case of 7x50 it is more than 7 mm. The dark adapted eye of a child can be as large as 8mm, adult have decreasing pupil diameter and at an age of 50 normally not more than 5mm. 8x30 is a good general purpose, reasonable size, easy to hold pair. For bird-watching you might want 10x, above that you will need a tripod.
The second number has a big effect on size, weight & cost; x30 are much smaller, lighter, cheaper than x50, but in dim light (dusk & dawn) noticeably brighter; in good light you wont notice the difference. I've switched to 8x40 from 8x50 for bird-watching.
The ratio of the two numbers (e.g., 8x30 about 4mm) should be less/equal to 7mm, because that is the size of the pupil of the eye wide open. Also, get ones with good coatings, multiple reflections can mess up the image, and 'eye relief' is very important if you wear specs.