People always wonder about a skunk in cribbage, another unique term. In case you are wondering a skunk has an unpleasant odour and in many sports if you are skunked it means you have been smelly or bad, generally losing by a lot of points or a large distance.
In cribbage to be skunked is to be beaten by 31 to 60 points and to be double skunked is to be beaten by 61 to 90 points and to be triple skunked is to be beaten by over 91 points (rare and almost impossible).
So you do not want to be skunked in cribbage and you want to skunk you opponent. In tournament scoring it counts as an extra match and a double skunk counts as an extra two, so the benefit is obvious – one more game towards winning a set and therefore a match.