Varnish Cache is a caching HTTP reverse proxy and web accelerator that you place in front of an HTTP server to cache content. It is aimed at content-heavy, dynamic websites and APIs and is configured with VCL, a programmable, compiled configuration language. It is self-managed software. Note the naming: the upstream project has been renamed Vinyl Cache (The Vinyl Cache Project), while Varnish Software maintains a distribution of it under the name Varnish Cache.
The software is open source under the BSD-2-Clause licence. Varnish Software, the company behind the distribution and commercial support, has its registered address in Stockholm, Sweden. Because you host the software yourself, you decide where traffic and cached content are processed, which makes it a suitable building block for a CDN of your own within the EU. Commercial products such as Varnish Enterprise and Varnish CDN are supplied by Varnish Software; for those, the contractual choice of hosting and support is relevant.