A tray was a flat surface used to transport and serve food.
In 2266, Janice Rand was accosted by the M-113 creature posing as Crewman Green as it attempted to get the salt off a tray of food she was carrying. Later, she delivered the meal to a very grateful Hikaru Sulu. (TOS: "The Man Trap")
Later that year, Lieutenant junior grade Joe Tormolen obtained a tray of food from a food synthesizer in a recreation room aboard the USS Enterprise. He placed the tray on one of the room's tables but an incident shortly thereafter, in which he accidentally stabbed himself with a knife from the tray, prevented him from eating the food on the tray. (TOS: "The Naked Time")
In 2267, Christine Chapel carried a bowl of plomeek soup to Spock on a tray. (TOS: "Amok Time") Later, she brought Ensign Garrovick a meal on a tray, in an attempt to coax him to eat something. (TOS: "Obsession")