The React Component API is a set of functions that allow users to access state changes, lifecycle stages, and rendering in their components. It provides various lifecycle methods such as `componentDidMount()`, which is called immediately after the component is added to the DOM, and `componentWillUnmount()`, which is called before the component is removed from the DOM. The API also includes functions for updating the state, such as `setState()`, which can be used with or without the `useEffect` hook. The React Component API offers a different method for creating components that access state without writing class components, as introduced in version 16.8 with Hooks.