Fair ball

From BR Bullpen

A fair ball is a batted ball that is not a foul ball. Generally, a fair ball is a ball hit in fair territory, but there is no definition of fair ball per se in the rules; what is a fair ball can only be construed from the definition of its opposite.

Section 2.0 of the Official Major League Rules defines a foul ball as follows:

A foul ball is a batted ball that settles on foul territory between home and first base, or between home and third base, or that bounds past first or third base on or over foul territory, or that first falls on foul territory beyond first or third base, or that, while on or over foul territory, touches the person of an umpire or player, or any object foreign to the natural ground.
A foul fly shall be judged according to the relative position of the ball and the foul line, including the foul pole, and not as to whether the infielder is on foul or fair territory at the time he touches the ball.
Comment: A batted ball not touched by a fielder, which hits the pitcher’s rubber and rebounds into foul territory, between home and first, or between home and third base is a foul ball.

Fair balls include balls that are hit out of play beyond the outfield fence (those are home runs).