Internetworking is connecting two or more computer networks with some sort of routing device to exchange traffic back and forth, and guide traffic on the correct path (among several different ones usually available) across the complete network to their destination. The devices used in internetworking are routers (originally called gateways, although that term was dropped due to confusion with functionally different devices using the same name), and some types of high end switches.
(Connecting together networks with bridges is sometimes mistakenly called internetworking, but this is not accurate, as the resulting system mimics a single subnetwork, and no internetworking protocol, such as IP, is required to traverse it.)
Internetworking started as a way to connect disparate types of networking technology, but it became widespread through the developing need to connect two or more local area networks via some sort of wide area network. The definition now includes the connection of other types of computer networks such as personal area networks.
The most notable example of internetworking in practice is the Internet, which is a network of networks running different low-level protocols, unified by an internetworking protocol, the Internet Protocol (IP). IP only provides an unreliable packet service across the internet; to reliably transfer data streams, a Transport layer protocol (such as TCP) must be used. This is part of why we commonly refer to TCP and IP together, as "TCP/IP". Some applications occasionally use a simpler Transport layer protocol (called UDP) for tasks which do not require absolutely reliable delivery of data, such as video streaming.