What is a modem?
A modem is a device that sends information between the outside world, or wide area network (WAN), and your home. Think of WAN as the Internet, and your modem as the entry gate to the Internet.
That's the simple explanation. For the more technically savvy: A modem is a device that turns your inbound connection (coax cable, telephone line, fiber optic line, or other) into an Ethernet connection, which allows a router to connect to the Internet.
Modems are usually provided by your internet service provider (ISP). Your primary Wifi point should be connected to a modem with an Ethernet cable.
Modem+Router combination devices
Many ISPs provide a device that includes both modem and router functionality. Connecting your primary Wifi point to these types of "combination" devices is fine. But for optimal setup you may need to adjust certain settings on the combination device to ensure your Wifi point is your network's primary router. Learn more about Double NAT
Don't have a modem?
Some apartment buildings and college dorms don't require a modem for Internet access. You can plug a router directly into your wall's Ethernet jack.