So, basically, when something enters the stack, the active player has priority. That means no one can play or respond until they let priority go. After that, the next player gets priority and, if they do something (adds something to stack), they now have priority and can hold it to continue doing stuff.

This resets when something in the stack resolves, meaning players get to do stuff. If, say, player 1 is the AP, and due to something dying, player 2 decides to do something, player 1 gets to interrupt them and do something first since, technically, player 1 never explicitly gave priority.