All messages between computers is sent by way of telephone lines, as there is already a network of telephone wires. But they were meant to carry voice recordings which is analog. On the keyboard we have digital. So we have to convert digital to analog (modulation) to send them over modems and reconvert to digital (demodulation) to see it on the screen. The device that does this is called a Modem (Modulator - Demodulator). In the early days, the modems were external to the computer. But now they are part of the hardware. External modems are available to connect to pay phones.
In digital 0 to 1 volts is 0 and 3 to 5 volts is 1. Analog is a sinusoidal wave. As the pulsations are predictable, a pure sin wave transmits no information at all. By varying the amplitude (height), frequency (number of waves per second), or the phase, a sequence of 0's and 1's can be transmitted. In amplitude modulation, two different voltages are used, for 0 and 1. A person listening to digital data transmitted at a very low data rate would hear a loud noise for a 1 and no noise for 0. In frequency modulation, the voltage level is constant, but the carrier frequency is different. 1 and 0 will yield two different tones. In phase modulation, neither the amplitude nor the frequency is changed, but the phase of the carrier is reversed 180 degrees when the data switches from 0 to 1 and vice versa.
For more details: Modems