I think that most people don't really even know what those names mean because they are not referred to by their names very frequently on The Muppet Show but if you've seen the show you know about the two grumpy old men that sit in the box seats and are highly critical of anything the Muppets perform on stage.
src
They were part of the original crew in the pilot episode of The Muppet Show and they remained as characters in every single episode although they were voiced / controlled by many different people over the years for a variety of reasons including and especially because of Jim Henson's death in 1990.
I think that fans of the Muppets don't have a full appreciation for how difficult it actually was for the people involved in these characters and basically any of the others as it involved the puppeteers and the voice actors to spend a great deal of time in close proximity to one another, especially on set.
src
If you are not familiar with these two the only reason I can think of that being the case is if you have never seen any episodes of The Muppet Show and if that is the case I highly suggest you rectify that situation as soon as possible.
Statler and Waldorf would constantly heckle the performers on the fictional stage and would almost always have a negative reaction to anything that took place. There are very few instances in which the "actors" on stage reacted to this criticism but Statler and Waldorf would return week after week often questioning why it is that they bothered to come.... again.
They make fun of everything and never laugh at any of the jokes that are told but feel as though their own jokes are hilarious, much like hecklers at real comedy shows.
There are a ton of compilations of these two hurling insults at the people and puppets on stage but I chose one of the shorter ones because honestly, there are hours and hours of footage of these two out there and understanding what they are referring to isn't very important.
I found them funny as a kid, but as an adult I kind of relate to their humor even more. That is one aspect of the Muppet Show that I think basically anyone who is familiar with it can agree with: It appealed to both children and adults even though it might have been for very different reasons.
src
I don't know exactly whose idea it was to include these two in the original lineup but after the overall show was very well-received it was actually these two that critics said they enjoyed the most. Keep in mind that this was the 1970's and Kermit, Piggy, and the rest of the gang were not even really known by anyone yet.
Here we are 50 years later and I can still return to these shows and enjoy them and there aren't a great many productions that I believe this is the case with. They, and most of the crew involved with The Muppet Show have a special place in my childhood and it is just so wonderful that Henson and Oz didn't give up when they were just getting started out and making very little money making commercials in the 60's, because it lead to iconic and timeless characters that will remain with us for a very long time.