setState is a public API, usually triggered in response to a user event like a click or an input change event.
State in React is local to a component, but it can be passed down to a component's children in the form of props.
Centralized state can be achieved using a library like Redux, where an individual component subscribes to an external data store's changes. Redux abstracts the details away, but under the hood it's still just setState.
The React API will also let a component decide for itself if it should be rendered.