The idea is that sometimes someone will post an answer and get the accepted answer award, even when it is obvious that someone else has an answer that is more correct. This can be done either through the OP's laziness in only awarding the check mark to the first decent answer, or because the OP just doesn't necessarily know better.
What I am proposing is a method for the winner of the check mark to pass it off to another answer on the thread. There have been a number of times where I have wanted to do this to someone who spent much more time and effort on their answer than I.
There have also been a couple of times where someone else in a thread was awarded the check, even though they themselves tried to tell the OP that mine (or someone else's answer) deserved it more than them.
In case I was unclear above, giving away the accepted check mark would also entail giving away the full 15 points that were rewarded along with it.