Modem is short for modulator/demodulator. What a modem does is translate the signals your PC makes into signals that can be sent over the telephone line.
Your PC produces a digital signal which are individual short pulses. However the telephone system was designed to carry an analog signal or audio signal which is a continuos electrical signal. These two signal types are incompatible.
This is where the modem steps in. It takes the digital signals your PC produces, and immediately translates them into analog signals and transmits them through the telephone lines. Conversely, it takes the analog signals from the telephone line, and translates these into digital signals that your PC can understand.
Modems also use a protocol or set of rules to communicate with each other. If both modems at each end are not using the same protocol, they will not be able to communicate with each other. The most common protocol today on high speed modems is MNP which comes various versions, the current being V.42 and V.42bis
MNP allows for high speed data transmission by using error correction (V.42) and data compression (V.42bis). Simply put, with error correction this protocol has very sophisticated ways of guessing what the data is if it was not transmitted properly. With data compression this protocol squeezes the data down to its bare essentials, stripping out any unnecessary characters.
MNP has 13 levels. The first four work no matter what type of modem you are talking to. However, in order for MNP to take advantage of the higher levels, it must be talking to another MNP modem.
Most modems are Hayes compatible which is the modem communications standard for the industry.
Finally, modems must use one of your PC's serial ports to transmit and receive through the telephone line. All modems can use any of the serial ports your PC comes equipped with. You determine this when you install your modem by setting dip switch or jumper settings.