In the parlance of the con operator, the big game is the whole of any con which itself includes a little game. Many confidence games use this method, although the most basic cons need use only charm and a bit of wit.
More specifically, the big game is that process wherein the grifter presents the mark with an opportunity which requires investment to exploit. In the case of the now-commonplace 419 fraud (see also Nigerian Mail Scams), the big game is the fraud itself: enticing the mark with millions of dollars if he would be willing to spring for the paltry few thousand dollars required to rescue/recover/export the outrageous (and non-existent) fortune from wherever it happens to be. The little game is the opportunity the mark sees: the exchange of a small sum of money for the reward.
This method is useful because, although people's kindness can sometimes be relied upon, desire (be it greed, lust or envy) makes a much more blinding draw. Especially greed.
The best plans can, of course, incorporate little game within little game. The purpose of this is that if one little game can be discovered by the mark, he might assume that since he sees two games, he sees the whole picture, when he is really indeed only seeing what he's supposed to see. There is still one more con lurking out there.
Many suspense movies (especially those of David Mamet) capitalize on this same twist: hints are dropped which lead the viewer to believe he understands what is going on behind the scenes, when in reality, the hints are only hints of a little game. Since the mark (in this case, the viewer) believes he knows what is going on, he is often lets his guard down a little more, thus making it even more difficult to see the big game.