A router is needed to share an internet connection, most routers though have 4 LAN ports so you can only wire in 4 devices. A hub or Switch (a switch is a slightly more intelligent hub) can take one of those router LAN ports and expand it further.. For example a router has 4 ports, wire in an 8 port hub/switch to one of those ports (via either a cable or homeplug) and your router now has the capability of sharing 10 wired devices to the internet instead of just 4..
In your case I was suggesting that you could leave the router downstairs and use one of the lan ports to run a cable upstairs/homeplug to a hub/switch. That then would give you 3 ports downstairs and however many the hub/switch has (minus one for the connection) upstairs
