As you probably know, the red light is absorbed fairly quickly underwater. Take a look at the RGB histogram of a picture shot in ambient light at some depth, and you'll see that the red channel is quite underexposed. At shallow depths, there's usually enough information in the red channel to restore it without unacceptable loss in image quality, but sometimes the red channel is so underexposed that restoring it is a bit of a challenge, and you'll get a lot of noise in the process.
If the red channel is severely underexposed, you can either increase exposure with the definite risk of burning out the blue and/or green channel, or you can put on a red filter, which effectively gives you the same effect (increasing exposure of the red channel), but without that risk of burning out the blues and/or greens. It comes at a cost, though: You have to use a larger aperture, a longer shutter speed or a higher ISO.
Of course, if you're deep enough that the red wavelengths are severely absorbed by the water, you'll need artificial lighting (e.g. a strobe) to get the true colors of the subject at depth. No filter can restore wavelengths that just aren't there.
Disclaimer: This is from a purely theoretical view and I haven't tried filters in practice. Yet. But I'm seriously considering that for available light shooting. For a more informed view from people with actual experience, you might like to read this and this article.