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In baseball, a fair ball is a batted ball that entitles the batter to attempt to reach first base. By contrast, a foul ball is a batted ball that does not entitle the batter to attempt to reach first base. Whether a batted ball is fair or foul is determined by the location of the ball at the appropriate reference point, as follows:

if the ball leaves the playing field without touching anything, the point where the ball leaves the field;
otherwise, if the ball first lands past first or third base without touching anything, the point where the ball lands;
otherwise, if the ball rolls or bounces past first or third base without touching anything other than the ground, the point where the ball passes the base;
otherwise, if the ball touches anything other than the ground (such as an umpire, a player, or any equipment left on the field) before any of the above happens, the point of such touching;
otherwise, (the ball comes to a rest before reaching first or third base), the point where the ball comes to a rest.

If any part of the ball is on or above fair territory at the appropriate reference point, it is fair; otherwise, it is foul. Fair territory or fair ground is defined as the area of the playing field between the two foul lines, and includes the foul lines themselves and the foul poles.^[1] However, certain exceptions exist:

A ball that touches first, second, or third base is always fair.
Under Rule 5.09(a)(7)-(8), if a batted ball touches the batter or his bat while the batter is in the batter's box and not intentionally interfering with the course of the ball, the ball is foul.
A ball that hits the foul pole without first having touched anything else off the bat is fair.
Ground rules may provide whether a ball hitting specific objects (e.g. roof, overhead speaker) is fair or foul.

On a fair ball, the batter attempts to reach first base or any subsequent base, runners attempt to advance and fielders try to record outs. A fair ball is considered a live ball until the ball becomes dead by leaving the field or any other method.

References

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^ Office of the Commissioner of Baseball (2018). "Definitions of Terms". Official Baseball Rules (PDF) (2018 ed.). Major League Baseball. ISBN 9780996114066.