This baseball term is used to describe a particular type of substitution. The double switch is most often used to replace an outgoing pitcher with a stronger hitter, and it is executed in two parts. First, the outgoing player, usually a pitcher who is up to bat soon, is substituted out for a position player. Next, another player batting later in the order is replaced, usually by a relief pitcher. The last step is for the two substitutes to swap defensive positions (if necessary).
The advantage of this strategy is that the batting lineup is strengthened, albeit temporarily, while using less players than a typical pinch hitter strategy. In the American League the designated hitter rule exists, which negates any need for the double switch. This rule is much more important to the National League, where it is used when a team needs to improve its offense quickly, in the short term. The double switch may only occur if the ball has been ruled dead.