The magnification number of binoculars is the focal length of the objective lens divided by the focal length of the eyepiece lens (used to magnify the objective image).    
http://en.wikipedia.org/wiki/Binoculars#Optical_parameters

This is exactly the same concept as telescope "power", and is extremely common knowledge among telescope users (who use several eyepiece lenses to vary power), but it is not very useful to binocular users to know.  Nevertheless, it is.

It does not compare to camera lenses which are used at prime focus (no magnifying eyepiece lens).

It is said that the binocular power number compares to the naked eye, that 7x power is 7 times larger than the eye sees, as if it were 7 times closer.  I cannot derive that definition.