Billy is a small monster who has appeared in a number of sketches during the first few years of Sesame Street.
He was seen as early as season 2 in a sketch where he, Grover, and Herry Monster demonstrated how three monsters remained three no matter where they stood. Fran Brill performed him here from a script (for Episode 0186) where he's referred to as a "Baby Monster".
Though often unnamed, he was most prominent (and referred to by name) in a sketch where he was confused about the concept of "here" and "there", and asked Grover and Herry Monster if they could explain it to him. As played by Jim Henson, Billy had trouble understanding their demonstration since every time he moves to where they instruct him to go, he is both here and there in relation to his previous location. When he finally gets it, another monster (performed by Richard Hunt) arrives to collect him.
He also appeared in a Grover sketch, getting into a boat with Herry, Fenwick and several other Anything Muppet monsters, and as a background singer in the original "C Is For Cookie." In another sketch, he and two other monsters Pamela and Fenwick demonstrate big, bigger, and biggest. (EKA: Episode 0443)
After years of absence from the show, he appeared in the 1989 special Sesame Street: 20 and Still Counting during Ray Charles's performance of Bein' Green. A couple years later, he appeared in the song "Small People", sung by Ziggy Marley.