Quick and simple answer to : What is computer networking?
The purpose of a network is to share resources, like files, applications, and printers. The purpose of a client-server network is to have at least one centralized server that manages the shared resources and security for the network users and computers.
In simplest terms, a computer network is created to share. In teaching computer networking I often commented that if you find someone who didn't like to use the computer network, they probably had a personal issue with the concept of sharing.
The Internet protocol suite commonly known as TCP/IP is a set of communications protocols used for the Internet and similar networks. You will often see the terms protocol suite or protocol stack used interchangeably. The protocol stack is an implementation of a computer networking protocol suite.
A Network protocol is a agreed upon set of rules that define how network computers communicate. Different types of computers, using different operating systems, can communicate with each other, and share information as long as they follow the network protocols.
The all encompassing footnote
I realize that I may have oversimplified some terms, but the goal was to deliver a basic understanding of the concept and not deliver a lecture on computer networking fundamentals. IMHO, many answers given to simple questions on online forums over complicate matters as well as add quite a bit of stray information.
These definitions were written off of the top of my head based on many years of networking experience. Any resemblance to Wiki or any other website is merely coincidental. (Since I am defining basic terms I would hope that they are at least similar!)