The 'use client' directive in Next.js is a special comment placed at the top of a React component file. It tells Next.js to treat that component as a client component, meaning it runs in the browser and can use React hooks like useState and useEffect. Without this directive, Next.js treats the component as a server component, which cannot have client-only features. In the example, the Counter component uses 'use client' so it can keep track of a count state and update the button text when clicked. The execution table shows the state changes and how the button text updates after each click. This directive is essential for adding interactivity in Next.js apps using the app router.