One player (the would be king maker) is sufficiently far down that they decide that their chances of victory, or second place, are negligable.
Then, either because they want to, or because they hope that pretending to do so will allow them to pull their chances up, they start pushing their support between the leading players.
If they still have sufficient power - they end up being able to choose which of the top n (usually 2) players wins the game.
Done well, it is an interesting politic as the two leading players vie for support and attempt to crush them (so that they can't decide) without weakening themselves overly.
Done badly (as in most games - and especially BabylonFive the CardGame) the two leading players end up with no say in the rest of the game - and might as well throw up their hands and say "Ok - so which of us do you choose to have win?"
Of course, the best solution to this is to have every player believe that they have a sensible chance of winning until it is too late for them to do this.