1st Rule in U/W Photography
The 1st and most important rule in underwater photography is to minimize the amount of water between your camera lens and the subject. As simple as that.
There are many reasons for which you would do this. The first would be that water consists of small particles (especially in low visibility) from which the light of the flash bounces back towards the lens, causing your image to feature a significant amount of backscatter. Backscatter seems as white noise in your images and doesn't flatter your subjects. Although backscatter can be minimized by using an external flash (for further information, please Click Here), coming closer to your subject, thereby reducing the amount of water between your camera lens and the subject, will significantly reduce the amount of backscatter you will find later on in your images.
The second reason would be the loss of color underwater. The closer you are to a subject, the less distance light needs to travel between the subject and your camera lens, which results with more colorful images. Subjects that are further away, will appear bluish. In addition, underwater strobes are usually effective for short distances, and therefore coming closer to your subject will ensure that it is positioned within an effective distance from the strobe.
The third reason would be a composotional one. Images in which your subject fills the frame are much more impressive than images in which the subject is too small in order to stand out from the background. In addition, when coming closer to your subject, details can be better seen and documented.
If you manage to rememeber and implement this 1st rule, you have already significantly improved your underwater photo results.