A router is a device to connect two networks together. In the case of most consumer routers, WAN(IE the internet) and LAN(your network) Routers also have the capability to connect to the internet without a computer. For example, it can make a DSL modem connect to the net without needing a computer to enter the password and such. Also, most routers have a switch built into them. THis allows you to connect multiple computer to it similar to a hub(or a plain switch)
A hub is simply used to connect many computers together with no additional featuers. Also, it isn't as fast as a switch, which, as I said, is commonly in a router.