Most of the names on the above cladogram are probably unfamiliar to most people. Those on the left represent various extinct clades of early vertebrate fish that lacked jaws. There are only two types of jawless fish living today: the hagfish (Myxini), and the lampreys (Petromyzontiformes). Neither of these jawless fish has a bony skeleton, but most of the fossil groups listed on the cladogram had a fairly extensive covering of bony plates. All of these jawless fish are traditionally placed in the order Agnatha ("no jaws"), but as you can see, this group is paraphyletic, including some but not all descendants of the common ancestor.
The remaining groups (Placodermi around to Sarcopterygii) are the Gnathostomata (Greek for "jaw-mouths"), what most people would call "fish". They include sharks, guppies, and lungfish to name a few. They differ from the earlier vertebrates in that some of the gill arches undergo modification in early development to become the jaw and its supporting structures.
The Tetrapoda (way down in the lower right of the cladogram) are the terrestrial vertebrates, and include most of the creatures you are familiar with: amphibians, reptiles, dinosaurs, birds, and mammals.
For more information about the relationships of vertebrate groups, try the Tree of Life page on vertebrates at the University of Arizona. Or, visit The Vertebrate Phylogeny Pages created by Jack Conrad.