An expression from game theory as developed by the Princeton mathematician Nash.
In common usage the word means a situation in which the gain obtained by one party is exactly equal to the loss suffered by the other party.
Say, there is a cricket match between India and Pakistan.
A bets with B a hundred rupees that India will win while B maintains that India will-not. Then B will have to pay a hundred rupees to A if India wins. Now whoever wins the loss suffered by one party is exactly equal to the gain made by the other party. This is a zero-sum game.
All games (more generally situations involving two parties) need not be zero sum games. Some can be win-win (where both parties make gains in different but equal ways), lose-lose, where both parties suffer losses (an extreme case would be an atomic war between two countries) and win-lose (where one party wins and the other loses). It is in this last category that some games can be zero-sum games.
A recent article in Time based on Wright's book The Evolution of God illustrates these different situations. (Time June 15 - 2009)