A double date was a date involving two couples.
In 2371, Tom Paris invited Harry Kim to go on a double date with him and the Delaney sisters, saying they came as a pair, and it was either both girls or neither. (VOY: "Time and Again")
In 2376, Neelix jokingly suggested he and Tom go on a double date; him with Baxial, his Talaxian freighter, and Paris with Alice. Paris quipped back, "You pack the picnic basket, I'll bring the deuterium." (VOY: "Alice")