I’ve heard the expression, “My dance card is full,” and knew from context that it meant someone was busy. I never really thought about the etymology of the phrase though. But today I was listening to a Librivox recording of Richard Marsh’s 1897 horror novel The Beetle and I recognized the source of the expression.
In olden times, at formal parties, people would schedule dances with each other. A person would have a card or booklet listing all the tunes that were to be played, in order, with a space to write in the names of dance partners. The Wikipedia entry has images of some cards.
This fascinates me because it is so alien to my experience, yet the expression is something I have known for a long time.