A modem converts the digital data signals into analog data signals. in simple language we can say it as a mediator to the server and client.
That's what the writer already said! It's amazing how fast technology moves on, I have not used one of these traditional modems for years, although a router is s modem really.
On an unrelated note, windows modems are absolutely horid, I remember them causing me major headaches trying to get internet access in posix based OS some time ago