The switch is an object that can be switched on or off (or only on) to complete objectives, control autoguns, control cameras, or (open,close, or toggle) a door. It's purpose in arcade is the same except it can't complete opbjectives. The objectives part can be only be done in Story or Assault.
In Ts3 the switch can also control Logic operations including light colour or behaviour, it can reveal items on the map, too. The design of the switch varies depending on which tileset is chosen.

TS3 Switch designs:
Egyptian - A set of ornate scales on a podium
Military - A more high-tech design which resembles a touch screen reacting to the heat imprint of a hand.
Lab - A simple design in which the top of the podium lights up when pressed
Horror - A lever switch bearing cogs and machinery, with a changing light on top.
VR - An odd design resembling a hole in a tree-trunk. It pulsates red and black like the rest of the map and the hole turns green when pressed.