The Opener
A reliever starts and gets the top of the order, then the bulk guy comes in.
How it actually works. The first inning is the only inning where the batting order is guaranteed, and it is guaranteed to be the best three hitters on the other team. An opener takes that inning, then the long man comes in and works through the middle of the lineup with the order effectively reshuffled in his favor.
Why it is done, and when it is wrong. The whole idea is a consequence of the times through the order penalty. If a pitcher is going to face the top of the order three times over five innings, and the third time is where he falls apart, then delaying his first meeting with them by one turn is free value. It looks like gimmickry and it is arithmetic.
What people get wrong about it. It costs a roster spot and it costs the bullpen, and a team that uses it every fifth day burns arms it will need in September. It is also close to unusable for a club with a genuine ace, because the whole premise is that the bulk pitcher is beatable the third time through.
Batter's Eye: look up anything in baseball