The example uses React and the react-dom library to render an SVG smiley face. It combines separate React components, `Eyes` and `Smile`, which contain complex SVG paths and shapes, with CSS classes for detailed styling. The main `App` component layers these on a yellow circle base, using SVG `transform` attributes to position, rotate, and scale the facial features. The code demonstrates how to compose and manipulate vector graphics programmatically within a React application.