React Router is an open-source library for routing in React apps that helps create and navigate between different URLs without page refreshes. It uses client-side routing to render components as the user navigates. React Router comes with three packages - react-router for peer dependency, react-router-dom for routing in React apps, and react-router-native for React Native apps. It provides different routers and the main components include routes, links, and navigation. Nested routes were simplified in version 6 by removing strict string matching.