A modem (modulator / demodulator) translates data streams for transmission.
If you dial up the net with an internet service provider, this can be and analogue or digital connection.
Analogue connections transmit audio signals – most should remember the ‚discussions‘ of modems at connection time (handshake), that one could hear, if he so desired. Usually a modem let the user hear the transmission with the connection partner until the connection was established. Afterwards it muted.
The convesion of the data stream into audio signals on one and the conversion of audio signals back into data streams on the other side is the task of modems.
A: 01000001 -> [ modem ] -> (sound) .. transmission .. (sound) -> [modem] -> 01000001 :B
With digital connections, there is not such a great difference. The data has to be prepared and converted. The key difference is, that there is no audio transmission, the information is transmitted digitally.