I thought the Wikipedia entry would cover this answer more thoroughly than I could:
The sweeper is a more versatile type of centre back who "sweeps up" the ball if an opponent manages to breach the defensive line. His or her position is rather more fluid than other defenders who man-mark their designated opponents. Because of this, the position is sometimes referred to as libero (from the Italian word meaning "free", as used by the sports journalist Gianni Brera). Though the sweeper may be expected to build counter-attacking moves, and as such requires better ball control and passing ability than a typical centre back, his or her talents are often confined to the defensive realm. For example, the catenaccio system of play, used in Italian Football in the 1960s, employed a purely defensive sweeper who only 'roamed' around the back line.
Some sweepers move forward and distribute the ball up-field, while others intercept passes and get the ball off the opposition without needing to hurl themselves into tackles. In modern football, its usage has been fairly restricted, with few clubs in the biggest leagues using the position.
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Their job is to cover for the outside backs and if the oncoming player gets past them it is then the sweepers job to try and get the ball.