PIste is a French word meaning "track" literally, like on a CD, in French you'd have "Piste 3" instead of "track 3".
For skiing it refers to what in the US you call "trails". Doesn't matter if it's groomed or not; any area that is marked for skiing is a piste. Areas that are left natural but still patrolled are called "itinerant pistes".
So skis are rated on their on-piste suitability as how well they perform on the groomed runs, off-piste is anything more natural.
And a flair is like an underflip in the pipe I believe, underflips are awesome because it's pretty much all I can do.