There's two big groups of four-limbed vertebrates: amphibians (like frogs), and amniotes (like us and birds). Amniotes developed into two groups: synapsids (mammals) and saurapsids (lizards, birds, turtles, etc.).

Dimetrodon was a synapsid that ruled the world tens of millions of years before the first dinosaurs evolved.

That makes it really cool, actually, precisely because it isn't a dinosaur. Dimetrodon is to us as brotosaurus is to chickens: a really interesting great great etc uncle.