the 32mm in this case, or the 2nd number in all binocs, = the diameter of the front/objective lens element.
This is the limiting factor of how much light the binocs let in. It is the measurement used for a binoculars aperture. You do not get a ratio like we do with f/stop on camera lenses, just the original objective lens mm.
You can still compare to the aperture rating on a camera lens,. in that is gives you an idea of the light gathering ability.
However it is obviously more directly related to the front element of a camera lens, which in ratio with the magnification, results in the aperture f/stop value of a camera lens. In both cases the larger the front element, all else being equal the more light, (and usually more detail.)
With all three of these new binocs having the same 32mm, the one with the lowest "X" rating, ie: the 10x, will have the best light ratio,. essentially the largest f/stop.
In camera lenses, a 200mm f/2.8 will have the same diameter front element as a 400mm f/5.6.
The same amount of light went in to both, but double focal length of the 400mm will half the f/stop.
I am simplifying the terms of course.