it's a little mini-server kind of thing that lets you connect multiple comptuers at your house to and share the single connection you have to the internet though your cable or dsl modem. if you connect 2 computers to your cable modem with just a hub, they will both try to get their own IP address and that is only allowed if you pay extra each month for most ISPs.
A router only has one IP address so technically it's the computer that is connected to the internet and shares it's connection internally with the computers in your network. In most cases it also provides a firewall to keep people from being able to get in through your modem and hack into your computer.
not all routers are wireless, but having the option makes sense so many retailers will only carry a couple models that arent.
there's a lot of different technologies that go into them such as the speed of the wired networking, the speed of the wireless networking, the wireless network encryption (if you keep the number of people using your connection down it will be faster, so even in the housing it's best to encrypt the signal and only let your roommates know the password). different types of encryption are different strengths of security, and the kind of password is different for each, one 8 characters of 0-9 and A-F, one has 16 characters the same way, others let you choose a password like the DIS does, but everyone that logs in has to see it, so don't choose any of your passwords for logging in to your computer or anything.
Thank you as well! Since again I know nothing about this and it sounds like I have a lot of options for a router, I think I may wait and see if my roommate brings a router and if she doesn't then I will convince one of my knowledgeable neighbors to come to the store with me to help me get one!