A button was a type of switch found on a piece of equipment which was operated by someone pushing it.
The Talosians, with their power of illusion, could make the crew of a spacecraft push any button which might result in the ship's destruction. (TOS: "The Cage")
In 2265, the mutating Gary Mitchell, for his own amusement, played with the controls of the bridge, such as pushing buttons. (TOS: "Where No Man Has Gone Before")