A dioptre in underwater photography terms is a supplementary positive lens that screws onto the front (usually) of your lens. In other words a positive screw on filter.
Dioptres are mainly used with domeports. Domeports act as negative lenses underwater because the shape of the air (glass) water interface is not flat. To correct for the negative effect of the dome we put a positive dioptre on the front of lens. The strength of dioptre required is determined by the diametre of the hemisphere that the dome and to a lesser extent by the positioning of the lens (its virtual aperture) within the dome. Dome manufacturers should tell you what dioptre you need with their port.
Of course you can shoot without a dioptre but you loose image quality in terms of colour saturation and contrast. We can't fit dioptres to the really wide lenses, but because of their large depths of field and angle of view we get away with it (14mm and fisheyes). Some people do use rear dioptres on these lenses.
Dioptres have also become increasingly common as macro accessories over the last few years. A positive dioptre fitted on a macro lens moves the focal range closer to the camera, meaning the lens will now focus beyond a 1:1 magnification, but will no longer focus on infinity.
Andi, a couple of years ago I wrote an article (with the help of Peter Scoones, BBC Blue Planet cameraman) in Underwater Photography Magazine on using wide angle zooms underwater that goes into domeport theory a bit, without getting too complex.
UWP Mag issue 5Not sure it is in simple english, but I hope this helps.
Alex