Varnish is a web application accelerator that provides an easy speed increase to most web applications and Drupal is no exception. It works by creating a reverse proxy service that sits in front of your web server and caches traffic that comes through it. When the page is requested, Varnish forwards the request to the web server to complete the request, the response that comes back from the web server is then cached by Varnish. This means that the next request to the same page is served by Varnish and not the web server, which results in a large speed increase.
The upshot of using Varnish with an application like Drupal is that when a request is made there is no hit to the web server (and thus PHP) and no hit to the database. Varnish works best with Drupal with anonymous traffic, as authenticated traffic requires cookies and custom HTML. Even so, you can see massive speed increases for any anonymous traffic on the site.