I'll also begin by issuing the disclaimer that I am not a doctor. I am, however, a biology student, and therefore can probably shed some light on the situation.
While I don't remember specifically remember hearing the term, the links provided by Robert give me a pretty good idea of what it means. A triblastic animal is a general term for any multicellular animal that forms the three embryonic germ layers (ectoderm, mesoderm, and endoderm) during the blastula/gastrula phase of development.
So what does it all mean? Well, I take it that in most contexts the term is used to differentiate between different multicellular organisms, much in the same way that we classify animals according to vertebrates/invertebrates. As a general rule, triblastic organisms are more advanced than their cousins who do not form the three germ layers during development.
The repeated mentions in articles about worms suggests that some worms are triblastic while others aren't, and so it is a convenient method of classifying them.
I hope this helps.
