A secondary control room deep in the original Enterprise and her sister ships, from which the vessel can be flown if the bridge is lost or seized.
Auxiliary control is the backup command centre of a Constitution-class starship. Set well away from the bridge, it has its own helm and navigation consoles and a viewscreen, so that the ship can be run from it if the bridge is destroyed, cut off or in the wrong hands.
In The Doomsday Machine the bridge of the wrecked USS Constellation is uninhabitable, and Kirk pilots the ship from her auxiliary control room, finally steering her into the mouth of the planet killer. In The Way to Eden, Dr Sevrin and his followers take over the Enterprise's auxiliary control and use it to divert the ship into Romulan space on the way to the planet they call Eden.
The idea carries on in later designs, most plainly in the battle bridge of the Galaxy class, and main engineering often plays the same part on other ships.