The term was coined by Rolling Stone writer Hunter S. Thompson to describe his (often extreme) reporting. Thompson himself would instigate events, often in a prankish or belligerent manner, and then document both his actions and those of others. The term has also come into (sometimes pejorative) use to describe journalism (or generally any writing) that is broadly in the vein of Thompson's writing, where fact and fiction were liberally mixed and his prolific intake of drugs and alcohol led to a febrile, run-on style.
Similarly, in pornographic movies, gonzo refers to productions where the camera operator or director take an overt part the action, either by talking to actors or by themselves being performers. Such movies often eschew narrative and plot, opting (as Thompson did) to present a roughly contemporaneous account of "actual" events. The intention of this partly to involve the audience in the action, in a manner similar to the theater technique of breaking the fourth wall (but also: it's cheap, and no-one has to remember any lines).
Gonzo or The Great Gonzo is a puppet character, one of Jim Henson's Muppets.
Gonzo is blue, with a long hooked nose. On The Muppet Show he performed as a stuntman and daredevil under the name "The Great Gonzo" (or "Gonzo the Great"). He takes pride in his iconoclasm, all the while romantically pursuing Camilla the chicken. A running gag related to Gonzo is that it's not clear what species he is supposed to be. In the film The Great Muppet Caper, he is shipped to England in a crate labeled "Whatever" (while Kermit the Frog and Fozzie Bear are labeled "Frog" and "Bear"). In Muppets from Space it is revealed that Gonzo is an alien, but it is not clear whether this is to be considered a canonical statement of Gonzo's origins.
