Skipping over the invention of the telephone and how it works, let's just assume that by the time you're reading this, hard-wired telephones still exist somewhere.
Because of the way the telephone companies grew up, they operated more or less like railroads -- the phone company owned the equipment, including the phones and the wires connecting them. In the U.S., that was one phone company, AT&T, who had a monopoly until the Justice Department broke the company up in 1982, creating smaller, regional companies and opening the field to competitors like MCI and Sprint. Because telephone lines ran into most American houses, it was a natural choice when people began linking computers together. On the fixed telephone system, all the parts worked together.
It was Bell Labs, a division of AT&T, who came up with the cell phone system, based on towers transmitting and receiving signals, forming "cells" of coverage that united to form a network. The cellular network, unlike the old hardwired lines, needed to have the ability to hand off calls as the recipient traveled between cells -- different antennas would take over, but as long as you were in a coverage area, you wouldn't lose the call.
When computers began to be connected over the telephone lines, they used a different method of exchanging information (see the sidebar on circuit and packet switching). For proponents of fixed mobile convergence, the challenge is to get these different systems, each requiring different hardware, to work together. But to do that, they all need to speak the same language.