In fanfiction terms, when someone has received a request to write something in particular, whether it is a simple thing out of every-day life or a longer story.
Anonymous made a prompt with character A and character B cuddling
Possibly the best day of the week in art class. It's the day that all people celebrate the beauty of life. It's great to be alive on prompt day!!
Katelyn: Today sucks.... I hate mondays.
Amy: But it's prompt day!!
Kayla: Oh muffins... prompt day fills my soul with glee!
Ryon & Will: Well... that was awkward.
Tessa: Shut up, nothing is awkward.... especially on prompt day.
Near as I can tell, it derives from DOS, where one would generally boot from their primary hard disk (invariably called the C Drive and be presented with a prompt that looked like "C:\>", indicating the drive they were on and their location in the directory tree.
Considered fairly obsolete, even amongst old DOS hats.