What is an external IP address?

An external IP address is the address assigned to you by your ISP (Internet service provider) that is how the Internet and all other computers outside your local network see you.
To give an example: each computer in a local network has been assigned to their own internal IP address by the router. The ISP is connected to the router and gives the router an external IP address that allows it to communicate with the Internet. While on the Internet, everyone sees your external IP address, but any information coming from the router is routed from the external IP address to the internal IP address.