Numbers that are counted backwards in fixed units from an arbitrary starting number to mark the time remaining before an event occurs.
On Danbooru, this usually refers to a series of images an artist or a group of artists draw with a number indicating how many days remain until a new character, event, product or series' release date or an old one's anniversary or birthday. They're usually indicated by "あとX日", meaning "X days left".
It's the opposite of event follow-up, which follows the progress of an event.
Often posted by official accounts with commissions from a variety of popular artists as a way of promotion.