Huh! I agree I hear it mostly on the internet, but I've never had negative associations with it. I'd roughly define it as the collection of themes, plot devices and motifs that writers frequently use in different genres, e.g. it's a sci-fi trope to meet an alien race whose society reflects in some way on our own, or it's a rom-com trope to have the lead character embarrass themselves in front of a date, etc. And while a trope could be clichéd, it doesn't have to be, if that makes sense.

TV Tropes - which, warning, is a horrible time-suck of a website - has a page on it here.

Within the context of this fest, I mean it in the sense of popular conceits and devices fandom uses in its fic, art and so on. Sometimes they're cheesy, sometimes they're kind of questionable, but I think they're all a lot of fun when done well.

Does that help?