Hello! The word "prose" can mean to "talk on tediously" - so to keep on talking in a very boring or uninteresting way. So if the person is talking about "listening to someone else in the office prosing on about the next big idea." it means that the person is talking continuously and tediously about some great idea that is actually very boring for the listener. I hope that helps!

I think it means something like: "going on" - "droning on" - i.e. talking about something in an extensive, detailed way - possibly over-extensive and over-detailed, to the extent that it becomes boring. You know when someone is telling a story in a lengthy way and you feel like saying "OK, get to the point- or, "OK, I get the point! The word prosing (from "prose") is used to contrast with a "poetic"way of expression. Poetry is often used to express complex ideas/ feelings etc in a short economical way - with few words. If you wanted to express the same ideas in prose (text, with full sentences) this might take much longer...