The first # is the magnification (power), the second is the diameter of the objective lens (the big lens). So your friend's binoculars were 10 power with a 50 mm lens
The naked eye has a magnification of 1x; a 10x lens will make objects appear to be 10 times closer.
The advantage of a big lens is more light is let in, making the scene look brighter. That is especially important under low light conditions. But lens quality also matters; coatings and the lens material itself also block some light, making the scene appear darker. The downside of a big lens is the whole thing ends up weighing more.
The usual "rule of thumb" is that a 7x or 8x is good for a handheld pair. By the time you get above 10x the shaking of your hands makes the image jump around a lot. Add in the rocking of a boat and it is hard to see an object, especially one at a distance. This is where stabilizing binoculars help out.
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