(covers information from several alternate timelines)
A torpedo bay is the area of a starship in which torpedoes are stored, and the torpedo launcher can be accessed by personnel. In the bay, torpedoes are removed from storage and placed into the torpedo tubes immediately prior to launch.
In the alternate reality, the torpedo bay of the USS Enterprise was operated manually by members of the crew. Two launcher cannons were accessible and six torpedoes could be simultaneously loaded into the torpedo tubes of a cannon. (Star Trek)
Different ships from the 22nd century to the 23rd century had varying degrees of automation of this process. The retrofitted USS Enterprise and USS Enterprise-A appeared to primarily use manually-loading bays (Star Trek II: The Wrath of Khan; Star Trek VI: The Undiscovered Country), while the process was more automated a century earlier on Enterprise NX-01. (ENT: "Fight or Flight", "Civilization", "Similitude") Vessels in the 24th century were also equipped with automated torpedo bays. (TNG: "In Theory") Even though 24th century torpedo bays were automated, they could still be modified for manual launch. This requires the person performing the launch to do it from inside the torpedo tube, causing plasma exaust to burn the person with severe plasma burns. (VOY: "Future's End, Part II")
The compact torpedo bay of the refit Constitution-class USS Enterprise-A was located on Deck 13. In 2293, Captain Spock and Doctor Leonard McCoy entered the torpedo bay, where they modified a photon torpedo to track the engine emissions left by General Chang's prototype Klingon Bird-of-Prey. When modifications were complete, they loaded the torpedo manually into its firing tube. (Star Trek VI: The Undiscovered Country)
Aboard the Galaxy-class USS Enterprise-D, the forward torpedo bay was located on Deck 25. (TNG: "In Theory") In 2368, Captain Jean-Luc Picard gave the winners of the primary school science fair a tour of several parts of the ship, including the torpedo bay. (TNG: "Disaster")
In 2372 of the mirror universe, Terran Resistance Forces engineers preparing for the launch of the ISS Defiant attempted to bring torpedo chambering mechanisms on-line in the aft torpedo bay. (DS9: "Shattered Mirror")