As far as I know, your hub handles the network connection between your two 'puters. A router handles quite the same but over the internet: the router manages (once properly configured) the internet connection and your two 'puters are linked to it; this way, your connection is shared between the two, and are still connected to each other (lan).
Hope it helps you.

A hub is basically just a way of connecting 2 or more networked computers together - they are non-intelligent, and at its simplest level, a hub could be thought of as a cable connector...
 
A router analyses the traffic coming into it, sees where the traffic is headed (what its destination is), and decides where to send it next. A router constantly updates it's internatl picture of what is going on in the network space around it, so it knows what other routers are available on the network, and what routers aren't working. This way, if one route between networks is broken, the router can send traffic over a different route, meaning that the data will get to where it is supposed to be going. It is because of this "intelligent" routing of network traffic that routers are used on the Internet, and why your route to a particular Internet site might be different from one day to the next.
 
Hubs are used within a LAN to connect computers together; routers are used to connect different networks (or different parts of the same network) together - e.g. separate offices on a WAN, or a connection to the Internet.
 
If you need a more in-depth explanation, you might want to look at a site called www.whatis.com
 
Rgds
AndyF