A peanut gallery was, in the days of vaudeville, a nickname for the cheapest (and ostensibly rowdiest) seats in the theater, the occupants of which were often known to heckle.
The least expensive snack served at the theatre would often be peanuts, which the patrons would sometimes throw at the performers on stage to convey their disapproval. The phrases "no comments from the peanut gallery" or "quiet in the peanut gallery" are extensions of the name.
In 1943 the Howdy Doody children's radio show adopted the name to represent its audience of children. Howdy Doody is most remembered for its later transition to television, which continued the Peanut Gallery audience, now on camera.
http://worldheritage.org/articles/Peanut_gallery