The Two-Headed Monster is a character from Sesame Street. They typically perform in skits that teach children how to sound out words, as well as how to cooperate to achieve a common goal.
Since 2004, they have appeared in various "Journey to Ernie" skits. In these skits, Big Bird would ask them if they have seen Ernie, only to get conflicting answers from each head. In Season 36, "Journey to Ernie" stopped appearing, which caused the Two-Headed Monster to disappear, and only appear in past inserts.