It may come as a shock to the average dino buff, but the Triassic, Jurassic, and Cretaceous eras weren't originally designated as a way to keep track of long-extinct dinosaurs. Rather, these enormous stretches of historical time were first marked out by geologists to distinguish among various types of geologic strata (chalk, limestone, etc.) laid down tens of millions of years ago. Of course, since dinosaur fossils are usually found embedded in rock, paleontologists associate dinosaurs with the era in which they lived—for example, "the sauropods of the late Jurassic."
To put them in the proper context, you should bear in mind that the Triassic, Jurassic and Cretaceous aren’t the oldest geologic periods, not by a long shot. First came the Precambrian, which stretched from the earth’s formation to about 542 million years ago. The development of multicellular life ushered in the Paleozoic era (542-250 million years ago), which embraced shorter periods like the Cambrian, Devonian and Carboniferous. It's only then that we reach the Mesozoic Era (250-65 million years ago), comprising the Triassic, Jurassic and Cretaceous periods. (Though they’re technically called periods, many non-scientists use the words "era" or "epoch" interchangeably.)
Next Page: The Triassic Period