A modem is a hardware device that allows a computer to send and receive data over a telephone line or a cable or satellite connection.
In the case of transmission over an analog telephone line, which was once the most popular way to access the internet, the modem converts data between analog and digital formats in real time for two-way network communication. In the case of the high-speed digital modems popular today, the signal is much simpler and doesn't require the analog-to-digital conversion.
A modem receives information from your ISP through your phone line or optical fiber cables in the form of analog signals. It then converts this into digital data so that it can be sent out to a computer or if you want many devices to use the same connection, a router.
It is important to remember that a modem is simply what converts the data between the outside world and your home.
While many modems are built into routers that allow the interpreted data to be ‘routed’ to more than one device within your home, a modem on its own won’t do this.