(covers information from several alternate timelines)
A galley was a section located on a starship that provided facilities for preparation of food. On some starships, a chef operated the galley, preparing cuisine for the crew and guests. In essence a galley is the naval and Starfleet equivalent term of a kitchen. With the advent of replicator technology in the 24th century, use of a galley fell out of use on most Federation starships, with occasional exceptions.
Enterprise NX-01 had a galley to supplement the use of protein resequencers with conventionally prepared food. Hoshi Sato discovered that this galley was protected by the Enterprise's Chef to the extent that it forced the cessation of her own cooking. (ENT: "Silent Enemy") The galley also featured a pantry. (ENT: "The Catwalk")
In 2371, in response to a need to ration replicator usage, Neelix established a galley on board the USS Voyager, by taking over the captain's dining room. (VOY: "Phage") The USS Bellerophon was also apparently modified in this fashion. (DS9: "Inter Arma Enim Silent Leges")
A galley was also present aboard the Krenim weapon ship. In 2374 of an alternate timeline, Annorax had dinner with Chakotay and Tom Paris. The galley prepared different alien food for this event. (VOY: "Year of Hell, Part II")