Hi, Philip - a piano party is when a group of piano players and friends gets together and plays for each other, or with each other. At the Denver party we all sit around and eat and talk, and whenever someone feels like it they sit down at the piano and play something. They think no one is listening, but when they're done everyone that's been congregating in the kitchen applauds and yells "well done!"
So the Denver one is very informal.
I've heard that at the European piano party a couple of months ago some people brought books of duets and they'd take turns sight-reading thru them with each other, besides the pieces they had "prepared" to play.
I gather from reading some of the posts here that some of the parties are more formal, and that while everyone may come each time, only a few will play at any given party, and it's set up so there's a formal audience, and then afterwards everyone eats and talks.
I think some of them are for people to share "works in progress" - sometimes even just sections of pieces they're working on, either to get used to playing before a formal recital, or to share tips and tricks.
So they differ from group to group, but they're all piano players playing for each other, and usually socializing and eating.
Hope that helps.