Varnish – also referred to as Varnish Cache – is an HTTP reverse proxy caching system – aka an HTTP accelerator.
Very basically, Varnish delivers fully rendered HTML pages very very fast. If this is configured to work alongside WordPress, you can make major monster speed gains, the like of which you only dreamt of a few short years ago!
In their words:
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.