NAT (Network Address Translation)

One public IP address to provide Internet access to many private IP addresses

The idea behind NAT lies in using one public IP address to provide Internet access to many private IP addresses. In other words, if you are connecting a company with twenty computers, you can provide Internet access to all twenty computers by using a single public IP address instead of twenty public IP addresses

Router that support NAT keep track of ongoing connections. They keep a table translating network addresses between internal and external networks. As seen in picture bellow:

An example of how a router with NAT can connect many devices with single public IP

Assuming that the router has infinite processing power, it can maintain ~65k simultaneous TCP connections.