The most obvious distinguishing feature of IPv6 is its use of much larger addresses. The size of an address in IPv6 is 128 bits, which is four times larger than an address in IPv4. A 32-bit address space allows for 232 or 4,294,967,296 possible addresses. A 128-bit address space allows for 2128 or 340,282,366,920,938,463,463,374,607,431,768,211,456 (3.4 × 1038) possible addresses.
In the late 1970s when the IPv4 address space was designed, it was unimaginable that it could be exhausted. However, due to changes in technology and an allocation practice that did not anticipate the recent explosion of hosts on the Internet, the IPv4 address space was consumed to the point that by 1992, it was clear a replacement would be necessary.
With IPv6, it is even harder to conceive that the IPv6 address space will be consumed. To help put this number in perspective, a 128-bit address space provides 655,570,793,348,866,943,898,599 (6.5 × 1023) addresses for every square meter of the Earth's surface.
It is important to note that the decision to make the IPv6 address 128 bits in length was not so that every square meter of the Earth could have 6.5 x 1023 addresses. Rather, the relatively large size of the IPv6 address is designed to be subdivided into hierarchical routing domains that reflect the topology of the modern-day Internet. The use of 128 bits provides multiple levels of hierarchy and flexibility in designing hierarchical addressing and routing that is currently lacking on the IPv4-based Internet.
The architecture of IPv6 addressing is described in RFC 2373, "IP Version 6 Addressing Architecture."