Version 4 IP addresses are 32 bits long. That allows for up to around 4 billion addresses; however, there are now far more than 4 billion devices that are using the Internet. There are two solutions to this problem:
1) Go to a new addressing scheme (Version 6 IP addresses), which are 128 bits long. This will potentially provide around 256 billion billion billion billion addresses, or
2) Arrange for a number of devices in a location to share the the same public address.
The first option is the eventual target, but there are a very large number of devices that are not capable of handling the version 6 addresses, so routers with Network Address Translation were devised to provide a solution that works with the devices that cannot easily be upgraded.
Although there are well over 4 billion different devices using the Internet, there are probably something like 2 billion different sites (buildings) that require unique public addresses.
A NAT router uses one public address and provides a private network that can support multiple devices all sharing the router's single public address. The following addresses are reserved for private networks:
10.0.0.0 to 10.255.255.255
172.16.0.0 to 17.31.255.255
192.168.0.0 to 192.168.255.255
These addresses are not allowed on the public Internet, so the same addresses can be used on different private networks without interfering with each other.
When a device on a private network sends a packet to the Internet, the NAT function in the router converts the sender's IP address to the router's public address and stores the details in its internal tables. When the reply comes back from the target site, the router recognises it and converts the address back again to the internal private address of the correct device.
When you use an IP address finder such as http://www.whatismyip.com it returns your public address, but when you look at the router's internal network or use a CMD based command you get the addresses relating to the private network.
If you have a separate modem and router, it is possible to use the Internet from a single computer connected to the modem without the router. In this case, you have only one address, the public address that will actually go right through to the computer itself.
I hope this helps.