The Lineup
Nine names in a fixed order that repeats all night, and the reason a hitter's spot matters at all.
What it actually is. The batting order is the sequence the nine hitters bat in, decided before the game and written on a card given to the umpire. It repeats: after the ninth man, the first bats again. A hitter cannot be skipped, and once a substitute replaces somebody he takes that spot in the order. Leadoff is first, cleanup is fourth.
What somebody who knows the game gets out of it. The old logic was speed first, contact second, best power fourth. The modern logic is that the first spot gets about eighteen more plate appearances a season than the second and so on down, so the best hitters go at the top regardless of how they look. Order is worth about one to two wins a season done well against done badly, which is small but free. The place it actually matters is avoiding traffic jams: a slugger with nobody on base ahead of him is a slugger hitting solo home runs.
The numbers worth knowing. The leadoff spot gets roughly 750 plate appearances over a full season, the ninth spot roughly 600. That gap of 150 is why the difference between batting your best hitter first and fifth is real, and also why it is not enormous.
What people get wrong about it. Cleanup is not the best hitter's spot any more and has not been for a while. The research points at second: enough men on base in front of him to matter, and nearly as many trips to the plate as the leadoff man. The clubs that put their best hitter second were doing arithmetic, not being clever.
At Little League and travel ball. Most youth leagues bat the whole roster in a continuous order rather than nine, which changes the job completely. There is no hiding a weak hitter, and the useful lever is not power at the top but on base ability, because in a six inning game with a run limit, avoiding quick innings is worth more than slugging. Batter's Eye has a Lineup Lab for both the professional and the GameChanger version of this.
Batter's Eye: look up anything in baseball