Fig.: to be in charge; to make the decisions; to exercise authority

He is surrounded by the best financial advisors, but when it comes to making the final decision he's the one calling the shots, because he is the B-O-S-S

Si è circondato di validissimi consulenti finanziari, ma quando si tratta di prendere la decisione finale è lui che comanda, perché lui è il Capo con la C maiuscola

You could be a rocket scientist, but here, in the gym, I'm the one calling the shots and you'd better do what you are told

Sarai anche un genio, ma qui, in palestra, sono io che decido e tu farai meglio a fare quello che ti viene detto

As long as I'm calling the shots, this project will never be approved

Finché comando io qui, questo progetto non verrà mai approvato

How come there's always disagreement and conflict in condo meetings? It's simple: everyone wants to call the shots

Come mai nelle riunioni di condominio ci sono sempre dissapori e litigi? Semplice: tutti vogliono imporre la propria decisione

It seems that there are a lot of supposed origins for this expression. From the sport of curling, which started back in Scotland in the 1500s, where the skip, or team leader, calls the shots for his fellow player, specifying distance, speed and line. Or from billiard, where the player calls which pocket will be used to sink a ball before hitting the cue ball. What about basketball, where the coach tells the players what play to make and what shots to take.
Then it may have military origins. It might refer to the commanding officer on a battlefield, who gives orders to the soldiers and calls the (gun) shots.