Binoculars always have two numbers in their name - such as 10x42 or 8x20. These two numbers refer to the binoculars' are magnification and lens size.
So with a 10x42 pair you have  binoculars with 10x magnification and a lens diameter of 42mm.
It is tempting to choose binoculars with the highest magnification - but this will mean they will be larger, and limit your field of view - making them harder to pinpoint some subjects. The higher the magnification, though, the harder it is to keep them steady - making the benefit of image stabilization even greater.
The second number is the objective lens size - with a larger lens making the image brighter which is particularly beneficial in low light conditions.
In practice it is the combination of the two numbers that actually tell you how bright the image will be. If you divide the lens size by the magnification you get what is known as the "exit pupil size". For a pair of 8x20 binoculars, the exit pupil is 2.5 – and for a pair of 10x42 binos it is 4.2. If you need to regularly use your image-stabilized binoculars in poor light conditions (say at dusk), then choose one where this ratio is 4 or greater.