The rate at which the batter gets a hit when he puts the ball in play. The calculation for BABIP is (H-HR)/(AB-K-HR+SF). League average is typically .300. A batter with a BABIP of greater than .300 is typically thought of as lucky (though batters with above average speed often have BABIPs greater than .300). A batter with a BABIP lower than .300 is often thought of as unlucky though batters with below average speed often have BABIPs lower than .300. As a rule batters have much greater variance in BABIP than pitchers.
Why does this stat matter for fantasy?
Unlike pitchers, there's no "normal" baseline for BABIP with hitters, as this can fluctuate greatly. A higher BABIP tends to mean the hitter produces a lot of line drives and a high exit velocity, which is a good thing for fantasy value.