The Internet began in 1969 when 4 computers were connected to each other over phone lines. Over the years, it has grown to millions of computers interconnected all over the world. On the Internet, there is a numerical string called an Internet Protocol address assigned to each device for purposes of communication under the IPv4 system. These numbers are 32 bit binary but they are usually displayed in human readable form as 4 sets of three digits each such as 172.16.254.1.

The Internet Assigned Numbers Authroity (IANA) manages the global allocation of IP addresses to 5 regional Internet registries who, in turn, allocate address to local Internet registries or Internet Service Providers. The growth of the Internet has outstripped the available addresses. The primary address pool of the IANA was exhausted on February 3^rd of 2011 when the last 5 blocks of addresses were assigned to the 5 regional registries.

Ipv6 is now being implemented to expand the pool of addresses for future assignment. The addresses are being expanded from 32 bits to 128 bits. They will look something like this: 2001:0DB8:AC10:FE01 in hexadecimal (the 16 digit based numbering system). This should be sufficient for the near future.

For more information, see this NPR article.