Varnish is a reverse proxy that sits in front of your web server and caches responses. When a request comes in, Varnish checks its cache first. If a cached response exists, Varnish returns it directly without touching Drupal at all.
This makes Varnish extremely fast. Cached responses can be served in microseconds, allowing a single server to handle huge traffic volumes.
Drupal integrates with Varnish through the Purge module and related submodules. These handle cache invalidation, telling Varnish to drop cached versions when content changes. Setting up Varnish requires some configuration work, but the performance payoff is dramatic. Specialised Drupal hosts like Acquia and Pantheon provide Varnish out of the box, which removes the configuration burden. For self hosted sites, Varnish plus a well tuned Drupal setup scales beautifully.