Welcome to Muppet Wiki!
The Question, similar in design to the Balloon-Head Conductor, is a tuxedo-clad character with a pink balloon for a head. Appropriately, the Question's balloon head has a big question mark where its face should be.
In the "At the Dance" sketch on The Muppet Show episode 115, George the Janitor asks Mildred if he can pop the Question. She says yes, so he does.