Babel Coder is a JavaScript library for building user interfaces using React. It promotes a declarative and component-based approach to building UIs that can learn once and write anywhere, as code written for React can target web, mobile, and desktop platforms. The document outlines key React concepts like components, props, state, events, lifecycles, hooks, context and more that Babel Coder utilizes to provide a simple and reusable way to build user interfaces.