From Muppet Wiki

H-Man is a charismatic game host, known chiefly for staging the "Sound of H Game" in Sesame Street episode 4115. Participants are prompted with a group of four objects, and are asked to isolate whichever one doesn't begin with the "H" sound.

H-Man is fond of the letter H, and has a tendency to make a spectacle whenever someone in his vicinity so much as utters a word starting with the letter.