Varnish is a caching tool that can speed up websites by caching HTTP responses in memory and skipping Apache, PHP, and MySQL for subsequent requests of the same URL. It works by checking if a page is cached and either returning the cached version or passing the request to the backend server to handle and then cache the response. While it does not support SSL or user state directly, there are strategies like SSL termination, excluding certain pages, and using Edge Side Includes to handle dynamic content and user sessions. A case study showed Varnish improved response times from 500-800ms to under 100ms for a site with major traffic spikes.