Gonzo the Great was a Muppet Show creation, namely a blue hooked nosed vaguely avian creature.
As the Muppet Show characters were all performers, Gonzo was... well.... the best way to explain him was part high culture wannabe, part Andy Kaufman style weirdo and part daredevil and 100% performance artist.
A typical “Gonzo the Great” routine would involve something like hanging by his nose high above the stage while reading Shakespeare or playing “Flight of the Bumblebee” while pole sitting.
It was a trope of the show that whatever Gonzo did was poorly received. Kermit the Frog would introduce acts by him alluding as much. Gonzo would often leave the stage early and angry yelling about “yokels”.
Unless he just went straight for the ludicrous such as reverse bungee jumping, using his indestructability as a Muppet to do insanely dangerous things.
A hyperkinetic and easily excited fellow, Gonzo typically appears near immediately with a “whoosh” sound effect. He is often accompanied by his girlfriends, an incredibly animated pack of hens.
One of the Muppet movies made it canon that Gonzo is actually an extraterrestrial which explains his core inability to fit in.