An incumbent is an official who holds an office. If you want to run for congress, you're going to have to beat the incumbent.
Incumbent comes from the Latin word incumbens, which means lying in or leaning on, but came to mean holding a position. It was first used in English for someone holding a church office, and then someone holding any office. You'll most likely hear it today for political officials. In a race for mayor, the incumbent mayor faces a challenger. Incumbent also means obligation. It is incumbent upon you to do the dishes.