SOLID OPAL - This means the opal is one piece usually a good thick stone
DOUBLET OPAL - "Double" 2 layers. Opal is glued to a backing of either black microscope glass, boulder opal, or dark potch. The reason for this is either the color bar is too thin making the stone unstable for setting or, the opal is crystal (see through) and the backing allows the color in the opal to shine.
TRIPLET OPAL - "Triple" 3 layers. In a triplet the opal is glued to a backing and a clear cap on top. Again this is usally done as the color bar is very thin, or, the cutter is getting more cut stones out of the one piece. Triplets are usually the cheaper range of opal as the opal content in a triplet can be very thin. However, these are ideal for souvenir jewellery and some rings as they can be more hard wearing with the cap on top. Just remember to keep them out of water which can affect the glue and spoil the look of your stone.