Modem stands for modulator-demodulator.
It is a device that modulates an analog carrier signal to encode digital information, and also demodulates such a carrier signal to decode the transmitted information.
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. Wireless modems convert digital data into radio signals and back.
Modems are generally classified by the amount of data they can send in a given time, normally measured in bits per second, or "bps". For example, a 56k modem can transfer data at up to 56,000 bits (7kB) per second over the phone line.
Faster modems are used by Internet users every day, notably cable modems and ADSL modems.
A modem works as an input and an output device because for outgoing signals it converts the digital signal into an analogue signal (modulation) and for incoming signals it works in the reverse way (demodulation).