In the world of jewelry, a triplet is a bit of lapidary magic, a way to make a lackluster stone (usually opal) into something beautiful. As the name implies, a triplet is made up of three parts: a dark background layer (often basalt), a thin layer of opal in the middle, and a clear quartz top. The layers are usually held together with a clear epoxy. It's like an opal sandwich.
A dark background can bring out color and fire in an opal which would not otherwise be apparent . Quartz, which is very durable, provides protection for the softer opal.
There is a bit of stigma attached to opal triplets. This is partly because in the case of most precious stones, making a composite such as a triplet is considered fraud. It should go without saying (but I'll say it anyway) that while opal triplets are considered a perfectly legitimate product, it is unethical to sell an opal triplet as an opal. Which is not to say that people don't do it. Caveat emptor.
There is also the fact that the color of an opal is mostly due to water contained in the stone, which can dry up over time, resulting in dullness. Of course, this is also true of solid opals, but a triplet may dull more quickly because it isn't exposed to oils in your skin which protect it from drying. Sometimes triplets can be badly made, too. They can be sloppily cemented, with too much or too little epoxy. Or the adhesive can be of inferior quality, and may turn yellow as it ages.
On the other hand, a triplet can be much more affordable, and just as beautiful, as a solid opal. And it has that protective quartz layer, which makes it more suitable for jewelry that is likely to get knocked around, such as rings.
If you're going to spend a significant amount of money* on a piece of jewelry, don't be afraid to ask questions. And don't be afraid to take your business elsewhere if you can't get the answers you're looking for. A competent, trustworthy jeweler should be willing to discuss your concerns.
*This is, of course, an entirely subjective term.
Source: my brain.