I have always understood the term donk to be short for donkey, and in poker to refer to jackass that is too stubborn (like a donkey) to release their hand when they should know that they are behind. The term getting donked or being donked, I would think, would refer to a situation in which a player being behind, and as someone else mentioned above, is not getting the right price to make the call, does so anyway and then sucks out on you.
In heavystack's example, I can't fault the villain for calling a pre-flop raise with pocket 8s. But when the flop comes 10-J-Q, I would think that villain would have to consider the kinds of hands that his opponent might have raised with. Considering the numerous combinations of cards from A-K down to A-10, K-Q to K-10, Q-J, Q-10, 10-J, or any hand with a 10, J or Q in it, he probably should have come to the realization that he was, more than likely, behind. So for him to make the call, I assume hoping for a 9 to give him a straight, would have been a donk call. For him to come over the top for all his chips was pretty much a donk a bet, considering that pretty much most of a lot of player's raising range (mine for sure) would not only have most likely put villain behind a bigger pair on the flop, but also given his opponent lots of bigger straight possibilities. In fact, we know that villain actually only had two outs and less than a 10% chance of winning the hand. The villain wouldn't know this for sure, but more than likely never slowed down to even consider the possibility. That is what makes donks donks. They don't try to put their opponents on hands, or see much of anything other than their own hands. So when villain hits the 8 to make a set on the river, I would definitely say that yes, heavystack, you got donked there.