What is IPv6?
IPv6 stands for Internet Protocol version 6. IPv6 governs the addressing and routing of data through a network.

IPv6 is intended to replace the IPv4 standard, whose limits on network addresses are beginning to restrict Internet growth and use, especially in China, India, and other heavily populated Asian countries]. But the new standard will improve service all around the globe; for example, by providing future cell phones and mobile devices with their own unique and permanent addresses.
IPv4 supports 4,294,967,296 addresses, inadequate for giving even one address to every living person, much less cars, phones, PDAs, and toasters; while IPv6 supports about 340 undecillion addresses.
Adopted by the Internet Engineering Task Force in 1994 (when it was called "IP Next Generation" or IPng), IPv6 accounts, so far, for just a few percent of the addresses in the publicly-accessible Internet, which is still dominated by IPv4. The adoption of IPv6 has been slowed by the introduction of network address translation (NAT), which partially alleviates the problem of address exhaustion. But NAT makes it difficult or impossible to use some peer-to-peer applications, such as Voice over Internet Protocol (VoIP) and multi-user games. Currently, the big drive for IPv6 is new uses, such as mobility, quality of service, privacy extension and so on. The U.S. Government has also specified that all federal agencies must deploy IPv6 by 2008.
Excerpted from Wikipedia http://en.wikipedia.org/wiki/Ipv6

Advantages of IPv6 over IPv4

1. Trillions of times more addresses will make it a mathematical certainty that in the future there will be orders of magnitude more devices with IPv6 than IPv4.
2. IPv6 is easier to configure. Neighbor discovery finds other IPv6 systems and stateless (and stateful) autoconfiguration enable more automated set up of systems.
3. IPv6 is compatible with 3G wireless (near) broadband and has other features that support greater mobility. There will be two billion mobile phones by 2006 and (at least) two addresses are required per mobile phone, so just enabling every mobile phone will require more IP addresses than are left with IPv4. Static addresses can also double battery life by not wasting power by checking whether a call is completed so the carrier can grab back the dynamic IP address, which wastes a great deal of power.
4. IPv6 supports ad hoc networking, given the features just mentioned, enabling many different people, vehicles, weapons, etc. to all become networked when brought into proximity without special programming.
5. IPv6 supports more efficient usage of broadband, both via the Jumbograms, in which packets increase from 64 KB in IPv4 to 4 GB in IPv6 (and soon 32 GB), and via the Flow Label, which enables network utilization to triple, from 27% efficiency to 81% efficiency.
6. Headers in IPv6 are leaner, with six unnecessary fields removed, and one entirely new field added, enabling more efficient routing.
7. IPSec is mandatory, bringing authentication (of users, of networks, and even of applications) to the entire IPv6 Internet and creating a “trusted bubble” according to Microsoft. IPv4 has no “trusted bubbles”.
8. Quality of Service is including in IPv6 headers, enabling premium pricing for guaranteed delivery, and prioritization of defense or other critical government Internet-based communications, even when networks are full. This is a big advance for actions against terrorist attacks or natural disasters, when virtually all communications channels are swamped and first responders and warfighters need prioritized packets to save lives.
9. IPv6 allows for many new possibilities, including a new geolocation system that lines up IPv6 addresses with squares or hexagons across the earth’s surface, in a new and novel latitude and longitude system that can be scaled down to nearly microscopic granularity, potentially
10. IPv6 allows for the possible new boom in new and novel applications to enter into the world. In some cases, IPv6 tips the balance toward upgrading vs. keeping an older version, as with Microsoft Longhorn. In other cases, IPv6 will enable completely new applications and systems of applications, such as IPv6 enabled conference badges, bar codes, or RFID tags.

There was also an IPv5, but it was not a successor to IPv4; rather, it was an experimental streaming protocol, intended to support voice, video, and audio.