The magnification is not a solitary measurement; in the case of optical SLR viewfinders in 35mm-format or APS-C, it's usually stated as "magnification with a 50mm lens focused at infinity" with the standard viewfinder optic diopter setting (no user correction applied).

It's only when all of those factors are taken into consideration: the focal length of the lens (which can be changed with the focus distance even without zooming, depending on the lens design) and the viewfinder diopter (adjustments for negative diopter correction will make the viewfinder image appear smaller, and positive will make it appear larger) that you can talk about magnification. And then it's pretty simple -- it's the apparent size of what you see through the viewfinder compared to what you'd see with the naked eye.

Ideally, I suppose, you'd want 1x (1:1) magnification with a normal lens so that when you're living the single-lens lifestyle you can easily shoot with both eyes open and everything matching in both eyes. That will almost always lead to some vignetting of the screen, though, and make the in-viewfinder data areas almost impossible to see without shifting your eyes around the finder's viewport. For this reason, the magnification is usually slightly less than 1x. (Some very-high-eyepoint finders, especially the lovely optional "sports finder" for the late, lamented Canon F1n, can be 1x or larger—but you could look through that sucker with both eyes.)

And because you're spreading a smaller amount of light over a larger area, a given magnification (with a purely optical system) will be significantly dimmer for a small sensor than it would be for a larger one (since the focusing screen is the same size, roughly, as the sensor). That's why, all else being equal (same screen design, same prism design and materials, etc.), a full-frame 35mm-format DSLR's viewfinder will be brighter than an APS-C's with the same magnification spec.

Electronic viewfinders, of course, can always pump up the brightness to compensate for the image magnification, but they still have to allow for the viewport problem in an eye-level finder—a 1:1 picture in the viewfinder is only helpful if you can see the whole thing.

The actual magnification of the viewfinder image will change, of course, when you change lenses or zoom. The specification, though, will give you some idea of the apparent size of the focusing screen -- a larger number means you will see a bigger picture through the viewfinder, and that can make composition a lot easier.