In photography terminology a "stop" is a factor of 2 in brightness.
For example if you reduce your aperture to 1/2 the area that's reducing by 1 stop.
If you dial your ISO (sensitivity) down from 200 to 100 that's 1 stop.
If you reduce your shutter speed by a factor of 2 that's 1 stop.
If you make your flash twice as bright that's 1 stop.
They're called stops because these controls on a manual camera actually have click-stops. You turn the aperture 3 clicks in one direction and your shutter 3 clicks in the other direction and your image brightness stays the same. Or you turn your ISO 2 clicks in one direction and your flash 2 clicks in the other direction and your image brightness stays the same.
Nowadays most modern equipment has click stops at 1/2 stop or 1/3 stop increments depending on the brand.
25 stops of range means the ability to resolve a dynamic range of 1 : 2^25.
It's not really bits per se, because the error in measurement also grows with the value, i.e. it can likely resolve the difference between a value of 1 and 2 but it cannot resolve the difference between 2^24+1 and 2^24+2.
