IPv4 and IPv6
Internet Protocol (IP) technology was developed in the 1970s to support some of the first research computer networks. Today, IP has become a worldwide standard for home and business networking as well. Our network routers, Web browsers, email programs, instant messaging software - all rely on IP or other network protocols layered on top of IP.
Two versions of IP technology exist today.

For readability purposes, humans typically work with IP addresses in a notation called dotted decimal. This notation places periods between each of the four numbers (octets) that comprise an IP address. For example, an IP address that computers see as

00001010 00000000 00000000 00000001
is written in dotted decimal as
10.0.0.1
Because each byte contains 8 bits, each octet in an IP address ranges in value from a minimum of 0 to a maximum of 255. Therefore, the full range of IP addresses is from 0.0.0.0 through 255.255.255.255. That represents a total of 4,294,967,296 possible IP addreses.
IPv6 Addressing Notation
IP addresses change significantly with IPv6. IPv6 addresses are 16 bytes (128 bits) long rather than four bytes (32 bits). This larger size means that IPv6 supports more than
300,000,000,000,000,000,000,000,000,000,000,000,000
possible addresses! In the coming years, as an increasing number of cell phones, PDAs, and other consumer electronics expand their networking capability, the smaller IPv4 address space will likely run out and IPv6 address become necessary.
IPv6 addresses are generally written in the following form:

hhhh:hhhh:hhhh:hhhh:hhhh:hhhh:hhhh:hhhh
In this full notation, pairs of IPv6 bytes are separated by a colon and each byte in turns is represented as a pair of hexadecimal numbers, like in the following example:
E3D7:0000:0000:0000:51F4:9BC8:C0A8:6420
As shown above, IPv6 addresses commonly contain many bytes with a zero value.Shorthand notation in IPv6 removes these values from the text representation (though the bytes are still present in the actual network address) as follows:
E3D7::51F4:9BC8:C0A8:6420
Finally, many IPv6 addresses are extensions of IPv4 addresses. In these cases, the rightmost four bytes of an IPv6 address (the rightmost two byte pairs) may be rewritten in the IPv4 notation. Converting the above example to mixed notation yields
E3D7::51F4:9BC8:192.168.100.32
IPv6 addresses may be written in any of the full, shorthand or mixed notation illustrated above.

ANOTHER DEFENITION ON IP ADRESS:

An identifier for a computer or device on a TCP/IP network. Networks using the TCP/IP protocol route messages based on the IP address of the destination. The format of an IP address is a 32-bit numeric address written as four numbers separated by periods. Each number can be zero to 255. For example, 1.160.10.240 could be an IP address.
Within an isolated network, you can assign IP addresses at random as long as each one is unique. However, connecting a private network to the Internet requires using registered IP addresses (called Internet addresses) to avoid duplicates.

The four numbers in an IP address are used in different ways to identify a particular network and a host on that network. Four regional Internet registries -- ARIN, RIPE NCC, LACNIC and APNIC -- assign Internet addresses from the following three classes.

Class A - supports 16 million hosts on each of 126 networks
Class B - supports 65,000 hosts on each of 16,000 networks
Class C - supports 254 hosts on each of 2 million networks
The number of unassigned Internet addresses is running out, so a new classless scheme called CIDR is gradually replacing the system based on classes A, B, and C and is tied to adoption of IPv6.