When you do something in turn, you do it in a certain order or one after another. Kids at a birthday party are supposed to take a swing at the piñata in turn, not to beat on it with sticks all at once.
When you take turns doing something, you do it in turn. Chess players have to move in turn, first one and then the other; and guests on a radio talk show have to speak in turn or listeners won't be able to understand what anyone's saying. The Latin tornus, or "turning lathe," is the root of turn, from the idea that your time to act (your turn) moves around in a cycle.