Ipv6 is the next generation of IP addresses. Like going from 3g to 4g on cellular phones, there will be a slight increase in efficiency of data transfer. This is not the main goal of ipv6.
We are currently using ipv4, which uses 32 bit addresses. Due to the limited amount of spaces provided by ipv4, we are literally running out. ipv6 uses a 128-bit address, making the number of addresses that can be assigned much larger than ipv4 could ever dream of assigning. This will end the need for network address translation, which was a hack thrown in to conserve space.
Ipv6 day is a worldwide release of the new protocol. Companies such as Google, Facebook, and Cisco will permanently give their users access to ipv6. This is a large step forward for ipv6, which is actually quite an old protocol (almost 13 years). The ipv6 will run alongside ipv4, so those stuck with ipv4 can still use the site's services.
Last year, there was a test of the protocol. It worked well, so the companies that participated began preparing for the final release of ipv6. This year, many companies are permanently dishing out ipv6 access.
This website will test to see if you truly have ipv6 enabled. If you don't it could be the fault of your internet service provider, of which many do not offer ipv6 yet. The Internet Society is urging people to contact their ISPs and recommend that they implement ipv6 as soon as possible.
Ipv6 may be a few more months or years away, depending on which internet service provider and type of computer you use. If you use Windows, you will need to upgrade beyond Windows 2000. The latest 3 versions of OS X are compatible. All versions of current Linux and BSD operating systems have ipv6 as they are commonly used for networking.