IP address
An IP address serves two principal functions. It identifies the host, or more specifically its network interface, and it provides the location of the host in the network, and thus the capability of establishing a path to that host. Its role has been characterized as follows: "A name indicates what we seek. An address indicates where it is. A route indicates how to get there."
The header of each IP packet contains the IP address of the sending host, and that of the destination host.
IPv4 shared address space
The use of shared address space is one of the various methods to allow transition from IPv4 to IPv6.
Its main purpose is to postpone the depletion of IPv4 addresses, by allowing ISPs to introduce a second layer of NATting.
Common practice is to give CPEs a unique IPv4 address on their internet facing interface and use NAT to hide all addresses on the home LAN.
Since public IPv4 addresses are growing scarce rapidly, it is no longer possible for some ISPs to assign unique IPv4 addresses to CPEs, due to the fact that there are none left to them.
Instead, an address in the range is assigned on the CPE's internet facing interface, and this address is translated again to one of the public IPv4 address of the ISP's core routers.
This scheme hides a large number of IP addresses behind a small set of public addresses, the same way the CPE does this locally, slowing down the rate IPv4 addresses are depleted.
The shared address space contains 2 or addresses, so each ISP is able to connect over 4 million subscribers this way.