Fair Ball
A batted ball inside the lines, and the moment the game turns live.
What it actually is. A fair ball is one that settles in the infield or that first touches the ground, a fielder or a base inside the first and third base lines beyond those bags. The lines are fair. Once a ball is fair, everything is live: runners can advance, fielders have to make plays, and every man on the field has a job whether or not the ball is near him.
What somebody who knows the game gets out of it. What separates a good defensive team from a bad one is almost entirely what the eight men without the ball do in the two seconds after a ball is ruled fair. Cutoff men move, bases get covered, pitchers back up bases, outfielders back up outfielders. That is what the Read the Play section of this site is about, and it is invisible on television because the camera follows the ball.
The numbers worth knowing. About seventy percent of plate appearances end with a ball in play. Roughly three in ten balls in play become hits, which is what BABIP measures, and that number is remarkably stable across the league and remarkably unstable for individual players.
What people get wrong about it. Fair or foul is judged by where the ball is when it is touched or when it stops, not by where it was when it left the bat or where it bounced first. A ground ball down the line that spins fair after bouncing in foul ground past the bag is foul; the same ball spinning fair before the bag is fair. This is the ruling that produces the most arguing per season on youth fields.
At Little League and travel ball. On a youth field with short fences and thick infield grass, a large fraction of fair balls never leave the infield, which is why the first thing worth teaching is not the swing but what the nine defenders do when contact happens. A 10U team that simply covers its bases correctly outperforms a team with better hitters.
Batter's Eye: look up anything in baseball