The site will tell if your Internet access will be fine on World IPv6 day. A positive answer means that you either have IPv4 only connection (no broken IPv6 DNS responses or routes), or have a fully operational IPv6 nameserver and route to the Internet. A negative answer means that your computer was tricked into using IPv6 while no actual IPv6 connectivity exists (and thus you are going to have problems on June 8th).
For a more detailed test: http://test-ipv6.com/