A modem is a device that modulates an analog carrier signal

Analog signal

An analog or analogue signal is any continuous signal for which the time varying feature of the signal is a representation of some other time varying quantity, i.e., analogous to another time varying signal. It differs from a digital signal in terms of small fluctuations in the signal which are...

 to encode digital information, and also demodulates such a carrier signal to decode the transmitted information. The goal is to produce a signal that can be transmitted easily and decoded to reproduce the original digital data. Modems can be used over any means of transmitting analog signals, from light emitting diodes to radio

Radio

Radio is the transmission of signals through free space by modulation of electromagnetic waves with frequencies below those of visible light. Electromagnetic radiation travels by means of oscillating electromagnetic fields that pass through the air and the vacuum of space...

.
The most familiar example is a voice band modem that turns the digital data of a personal computer

Personal computer

A personal computer is any general-purpose computer whose size, capabilities, and original sales price make it useful for individuals, and which is intended to be operated directly by an end-user with no intervening computer operator...

 into modulated electrical signals in the voice frequency

Voice frequency

A voice frequency or voice band is one of the frequencies, within part of the audio range, that is used for the transmission of speech.In telephony, the usable voice frequency band ranges from approximately 300 Hz to 3400 Hz...

 range of a telephone

Telephone

The telephone , colloquially referred to as a phone, is a telecommunications device that transmits and receives sounds, usually the human voice. Telephones are a point-to-point communication system whose most basic function is to allow two people separated by large distances to talk to each other...

 channel.