This article is from the of the muppets FAQ, by Craig Silverstein with numerous contributions by others.
Muppets are puppets invented by Jim Henson and his colleagues. Muppets were specially designed to be on television and in the movies, using camera techniques as well as classical puppeteering techniques to create the illusion of life. Many Muppets are hand puppets with arm wires. However, Muppets now include the most advanced computer and animatronics technology. For the purposes of this newsgroup, "Muppet" covers anything that has been created by The Jim Henson Company or the Creature Shop, including creations in "Muppets Tonight!," "The Muppet Show," "Sesame Street," "Fraggle Rock," "Dinosaurs," _The Dark Crystal_, _Labyrinth_, _Babe_, etc.
Here's Jim Henson's take on the question, from an interview by Judy Harris (full text is at http://www.bestweb.net/~foosie/henson.htm; the article that came out of this fascinating interview is in the April/May 1983 issue of _Cinefantastique_): "Well, to me the Muppets are sort of fuzzy, bright colored, cute, lovable caricatures." He's explaining why, to him, the creatures in _The Dark Crystal_ aren't Muppets. But we don't listen. La la la, we go.
In the same interview, Henson talks about the origin of the word "Muppet": "It was really just a term we made up. For a long time I would tell people it was a combination of marionettes and puppets but, basically, it was really just a word that we coined. We have done very few things connected with marionettes."