A React component renders an SVG circle that follows the mouse cursor across a 960x500 viewport. The circle's center coordinates are updated through React's `useState` hook and an `onMouseMove` event handler, which captures the `clientX` and `clientY` positions. The app initializes the circle at the viewport center and redraws it with a constant radius of 30 pixels on every mouse movement, using React DOM to mount the component into the page.