It's true, a modem and a router are two separate things and they do different jobs. However, a router would be useless without its in-built modem capabilities.
A modem provides you with internet access. A router allows you to have more than one computer using the same internet connection and if your computer has wireless capabilities, you don't even need a cable connecting you to your router, it can connect wirelessly.
A router must still connect to the internet though, so it's basically a modem with extra features that transmits signals that allow the wireless connections as well as allowing multiple computers to connect at the same time. Nifty little things aren't they?
Check out our iiHelp article Wireless explained for more information.