They are a troupe of vaudeville performers and actors who put on a regular show called "The Muppet Show", which is televised worldwide.
The leader of the Muppets is Kermit the Frog. Although meek and shy, Kermit manages to keep the wild and unstable personality of the other Muppets in check, although there are several hints that he may be as crazy as the rest of them.
The Muppets are goofy, silly and wacky, often using logic that seems incomprehensible.
The Muppets have a degree of invulnerability, as they are able to bounce back from things that would be fatal and/or traumatic to most humans.
At the beginning of The Muppets, the Muppets have disbanded, thinking that the world doesn't care about them. Thanks to the efforts of Walter, Gary and Mary, the Muppets are able to realize that the world still cares about them. Thus, they reunite, and bring back "The Muppet Show". As a sign of gratitude, Walter is made into a member of the Muppets.
The Muppets are known far and wide across the world, which why they are often able get celebrities to help them, even if those celebrities sometimes get caught in the crossfire of the Muppets' wackiness (in one notable example, one of Dr. Bunsen Honeydew's invention accidentally made Brooke Shields grow to giant size until she was as big as the room).