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It's a punch down terminal for cat5 wire for phone. My guess is that they used cat5 for telephone jacks in every room. Go to one of the rooms and see if you can plug a network cable into the jack if you can't (because it is too big) then its a rj11 jack for phone. I use these terminal for phone. The orange twisted pair on the back is looped to every orange wire.
I would recommend running wireless if you want to get up an running quick. There is a way to convert the cat5 into phone and Ethernet but it take some know how and would not be something that I could walk you through over a forum unless you have some experience.