Before the Cambrian period, 600 or so million years ago, life on earth consisted mostly of single-celled bacteria and algae--but after the Cambrian, multi-celled vertebrate and invertebrate animals dominated the world's oceans. The Cambrian was the first period of the Paleozoic Era (542-250 million years ago), followed by the Ordovician, Silurian, Devonian, Carboniferous and Permian periods; all of these periods, as well as the succeeding Mesozoic and Cenozoic Eras, were dominated by the vertebrates that first evolved during the Cambrian.
For whatever reason, the Cambrian witnessed the appearance of some truly bizarre creatures, including the five-eyed Opabinia, the spiky Hallucigenia, and the three-foot-long Anomalocaris, which was almost certainly the largest animal ever to appear on earth up to that time. Most of these creatures left no living descendants, which has fueled speculation about what life in succeeding geologic epochs might have looked like if, say, the alien-looking Wiwaxia was an evolutionary success. The Cambrian period marked the appearance of the earliest identified vertebrate organisms, including Pikaia (which possessed a flexible "notochord" rather than a true backbone) and the slightly more advanced Myllokunmingia and Haikouichthys. Essentially, these three genera count as the very first prehistoric fish, though there's still a chance that earlier candidates may be found dating from the late Proterozoic Era.