An Ethernet printer will plug into an Ethernet network via an Ethernet cable. Your router acts as the hub of your personal Ethernet network in your house. Depending on the router and firewall settings on the machines, you could plug an Ethernet printer into one port of the router and it should appear on the network. This restricts the printer to being co-located near the router. Since it involves firewall settings and router configurations this setup can be confusing.
A wireless printer has a wireless router built into it and will appear to your desktop computers as another wireless network to which you can connect. They are usually more expensive but they are also more flexible. You can unplug the things and move them around the house as needed.
The following URL takes you to some tutorials at the HP web site on Wireless printing.http://www.hp.com/united-states/campaig ... ningTools/
If it was me I would buy a wireless printer.