A set of technical detail imprinted on any pair of binoculars could be something like this: 7×50, 8×20, 8×42, 10×25, 10×50 or 12×50, as can clearly be seen in the image (from Wiki).
The first number (7, 8, 10, 12) is the magnification number, the “power” of the binoculars. The object is magnified by 7, 8, 10 or 12 times, which means that it appears to be 7, 8,10 or 12 times closer than seen with the naked eye. So, the higher the magnification, the more detail the viewer is supposed to get.
However, there’s more to binoculars than simply looking for the more powerful instrument.
More power comes at a price:
1. Higher power translates into a smaller exit pupil (see elsewhere), which means that, even though you will have more detail, the image seems to be less clear – in particular in dim conditions.
2. The higher the magnification, the more any movement is enhanced. This means that it becomes more difficult to view an object, since even the slightest hand movement is exaggerated as well.
3. More power also impairs field of view, which means picking up an object and following it will be more difficult.
4. More power also restricts depth of field. (see elsewhere)