Computer communication is the transmission of data and information over a communications channel between two computers, which can be several different things.
Communications between computers can be as simple as cabling two computers to the same printer. It can be as complex as a computer at NASA sending messages through an elaborate system of relays and satellites to tell a computer on Mars how to drive around without hitting the rocks.
Depending on the context, for computer communications you might use the terms:
Data Communications for transmission of data and information over a communications channel
Telecommunications for any long-distance communications, especially television
Teleprocessing for accessing computer files located elsewhere
A communications channel, also called a communications line or link, is the path that the data follows as it is transmitted from one computer to another.
Below is an animation of a communications channel at work. A PC is sending a message to a web server clear across the country. Notice the variety of transmission methods used: telephone lines or TV cable lines, satellite links, microwave relay. This is a simplified version of what really goes on! (The animation runs 10 times and stops. To restart it, use your browser's Refresh command.)