React is a JavaScript library for building user interfaces and single-page applications. It allows developers to create reusable UI components called elements that can be rendered to the DOM. Components can contain state that updates the UI and respond to user events. The key concepts in React include JSX for building UI elements, components, props for passing data between components, and state for dynamic data. Setting up a React project involves installing dependencies like React, ReactDOM, and Babel to transpile JSX and enable component-based development.