React component states are dynamic objects that, unlike props, are managed internally within the component and can change in response to user actions, network activities, or other triggers, significantly influencing a component's behavior and rendering. Components with states are called stateful components, while those without states are stateless. Initial states are typically set in the constructor method using `this.state`, and updates to the state should be done using the `setState()` method, as directly modifying `this.state` outside of the constructor does not trigger a rerender. The `setState()` method schedules state changes and requests React to update the component and its children accordingly, enhancing performance by batching updates. However, calling `setState()` must be done cautiously within React lifecycle methods to avoid issues such as infinite loops, particularly in `render()` and `constructor()`, which should not include `setState()`, whereas methods like `componentDidMount()` and `componentDidUpdate()` can incorporate `setState()` under specific conditions.