A Modem gets it's name from modulator and demodulator which are the functions that it does. For a modem to transmit data it encodes the digital information to make it easier to transmit, and then when it receives encoded information is demodulates it which basically means it translates it.

To send information a modem converts digital to analogue and then to receive information again it converts analogue to digital.
In the case of a standard dialup modem that is why if you ever lift up the telephone receiver when you are connected to the internet you hear lots of strange sounds. These sounds are the analogue signals going down the telephone line both being received and transmitted.

There are now mobile broadband modems that are used to deliver broadband via mobile phone networks.