A zero sum game is a game in which the players can only accumulate a profit from the other players loses. This means that the net profit of any player(s) can only equal the net losses of the other player(s).
Zero sum games are also known as constant sum games. They get that name because it does not matter if the sum of the payment equal zero but more importantly the total is the same for all outcomes.
An example of a zero sum game in the financial world would be an option writer. An option writer can only make a profit from the losses incurred by the holder of the option. If an investor tries to outperform on a zero sum game it is balanced by outperforming losses on other end of the investment.