What does no comments from the peanut gallery mean?

Answer 1

It is referring to uneducated persons responding or throwing out critisism. Also referring to the least expensive seats.

Answer 2

The "peanut gallery" is the highest level of the balcony in a theater, with seats which are the furthest from the stage or screen. These are therefore the cheapest seats, catering to the poorest theater-goers, often children. In days gone by, people in these seats would throw peanut shells at the more affluent members of the audience below them, sometimes simply to irritate them, sometimes to indicate displeasure with the show being presented. Therefore, "no comments from the peanut gallery" means: "Unless you intend to take this situation seriously, please do not comment on it, especially in a rude or uninformed manner." Children are often the target of this admonition.