Camera settings, high shutter speed or small apertures or a combination of both. If the picture is of a fish swimming normally, most likely it was shot during the day, because most fish are asleep at night.
This started in the Nikonos days, when depth of field (areas in focus) was needed to help make up for the lack of focusing of that rangefinder camera. So the photographer had to stop down (smaller aperture) in order to help save an out of focused picture. The smaller aperture under exposed the background (blacken), so the only light hitting the film was the light from the strobe.
Fast forward 2005, we now have some great PS digitals with some of the best autofocusing and exposure features and some are still stuck in this mode.
For myself, I look for a more balanced lighting, a more natural look. Where the background and foreground is very close in exposure. Like what you would see in an actual dive (Plus the added colors) !
My opinion is that the strobe manufacturers are pushing expensive single strobes that are much too powerful at such a close distance. Lower power settings and diffusers will help, but an even bigger help would be to design a strobe with 3 or 4 flash heads, controlled power settings. To "wrap" light around the subject and the soften the harsh shadows. The lower strobe power will also enable you to open up the aperture to get the background "out of the black", without over exposing the foreground.
Dive Safe