A date or rendezvous was a meeting of two individuals with a romantic intention.
Geoff Miles, a fourth grade student from Worley Elementary School, asked the question to the crew of Enterprise NX-01, "Is dating allowed on Enterprise?" to which Captain Jonathan Archer replied "Well, it's not discouraged, but there isn't a lot of privacy on a starship. Most of our crew share quarters with at least one other person, so it wouldn't exactly be practical. But if two crew members decide that they really like each other, there are a lot of places they can go to look at the stars." (ENT: "Breaking the Ice")
In 2373, Tom Paris and B'Elanna Torres had a lunch date which ended up getting postponed or canceled when Torres became engrossed in the holographic program Insurrection Alpha and forgot about the date. After Paris discovered her using it, he asked her to reset it so that he could try it out, pointing out that he had be on the USS Voyager's bridge in half an hour. (VOY: "Worst Case Scenario")
In 2375, Chakotay, while posing as Jason Hayek to infiltrate the training simulation on Terrasphere 8, used a tactical report due in the morning as an excuse to finish his date with "Valerie Archer". (VOY: "In the Flesh")