The document I'm working on is a report that is due next week and the deadline is fast approaching. A "deadline" is the date when something must be finished. My report is due next week, meaning that the deadline is next week; I must complete it by next week. When I say the deadline is fast approaching, I mean that we have a lot of work to do in a very short period of time between now and the deadline; the deadline is "coming up soon," we could also say. Something that is fast approaching can be something positive or negative. If your birthday is next week, you may remind your friends that your birthday is fast approaching. Depending on old you are, this is a good thing or a bad thing!