Varnish Cache is a web application accelerator also known as a caching HTTP reverse proxy. You install it in front of any server that speaks HTTP and configure it to cache the contents. Varnish Cache is really, really fast. It typically speeds up delivery with a factor of 300 - 1000x, depending on your architecture.
Varnish speed up Drupal sites through caching. In a single-server setup, Varnish sits at port 80 (rather than Apache) and calls out to Apache only if the request URL isn't cached or if another set of conditions are met. Those sets of conditions are usually spelled out in the default.vcl configuration file.
In order to set up Varnish on my latest Drupal 7 project, I needed to put together documentation from a lot of different places.