Really, I don't think we needed a whole thread on this, but I've read quite a bit of GM analysis, and they usually consider a variation refuted when one side (more severe if it's black) can get a decent advantage. Once it's clear that a move leads to a pretty decent white advantage, they tend to at that point use the term refuted.
Really, what do you mean: "refuted" or "refutation"?

I agree with the first part: the one for black, but in the case for refuted for white, it doen't work that way. It is still considered that the game before the first move is played is drawn- no one has been able to prove otherwise for the time being. Therefore to refute a white opening black must have decisive advantage as well.
We certainly have the mental capabilities to call a bad position bad even if we haven't found a forced mate. An opening is refuted if the general consensus can smell the stink of the resulting position. There may be chances to draw, and of course even to win (anything can happen!), but why play it if there is something better? I think this is the point of the "refutation" label, at least how its used in chess literature.
I'm starting this topic because another thread that I started a few days ago (see link below) has drifted off on to this topic and so it seems to justify its own thread.
So in my opinion: For Black, a defense should be considered to be refuted if a decisive advantage can be demonstrated leading, eventually, to his mate.
For White, an opening can be considered to be refuted if black can demonstrate that with best play a draw or a decisive advantage for black can be demonstrated.
http://www.chess.com/forum/view/chess-openings/has-any-1st-move-for-white-or-black-ever-been-refuted?page=1