The word "modem" is a contraction of the words modulator-demodulator. Which is exactly what a any modem does.The sending modem modulates the data into a signal that is compatible with the phone line, and the receiving modem demodulates the signal back into digital data. Modems came into existence in the 1960s. The initial speed of these modems were about 300bps. The reason this speed was tolerable was because 300 bps represents about 30 characters per second, which is a lot more characters per second than a person can type or read.

56 Kbps - Became the standard in 1998.
When a modem first makes a connection, you will hear dialing sounds coming from the modem. These are digital signals coming from the computer to which you are connecting being modulated into audible sounds. The modem sends a higher-pitched tone to represent the digit 1 and a lower-pitched tone to represent the digit 0. At the other end of your modem connection, the computer attached to its modem reverses this process. The receiving modem demodulates the various tones into digital signals and sends them to the receiving computer. The process is a bit more complicated than sending and receiving signals in one direction and then another. Modems simultaneously send and receive signals in small chunks. The modems can tell incoming from outgoing data signals by the type of standard tones they use.

56k Modem Speeds
A modem that communicates at 56 Kbps downstream and 33.6 Kbps upstream is the standard today. It is intended for use only with an ISP that is digitally attached to the telephone system. Most service providers are typically connected with high-speed digital T1 or T3 circuits.