Delicacies were specific foods and beverages that were considered by specific cultures to be specifically fine and or valuable.
According to Jean-Luc Picard, caviar was "a delicacy from the Caspian Sea on Earth. It's a favorite of mine. Our replicator's never done it justice, but I managed to store a few cases for special occasions." (TNG: "Sins of The Father")
Falah nectar, a beverage made from a meat byproduct, was considered to be a delicacy by the Nar Shaddan, an alien species from the Delta Quadrant. (VOY: "Workforce")
The Terellian pheasant was a fowl whose meat was considered to be a delicacy. (VOY: "Warhead")