A Superclass within the subphylum Vertebrata; it consists of Amphibia, Sauropsida (Reptilia, Aves, et al) and Mammalia. It excludes Osteichthyes, Chondrichthyes, Placodermi, and Agnatha.
The simplest way of defining this group is as animals that have four limbs (chiridii) with digits on the end (although in some cases the limbs/digits appear only in the skeletal structure, for example the flanges in a whale's flipper. And to make things more complicated, snakes are also tetrapods). While other animals may have four limbs, all existing tetrapods have five digits per limb, or have descended from something that did.
http://tolweb.org/tree/eukaryotes/animals/chordata/acanthostega/tetrapod.lichen.a.html has an essay on the exact definition of Tetrapoda.