Howmar,
Upon detailed examination of my new 2552 that I picked up in February, I noted the same situation regarding the distribution box. One of the things I did was pull the DVD "Theater" unit out of it's slot to allow me to trace wiring and cables and make a connectivity diagram for future reference for all the electronics that I could trace. Assuming our 2552's duplicate, what I can tell you is that the distribution box is non-functional as delivered. As noted in above posts, it has outputs connected and is connected to 12-volt power, but currently has no input. In my unit, the box is the same AVS050SD unit that Volkeman posted the photo of; the two outputs are connected to the two left-most connections. The output furthermost to the left runs to the "Component/AV In" connection on the front Samsung 32" TV. The output next to it runs down behind the DVD cabinet wall. Although I couldn't trace it further, I'd bet that it runs back to the vicinity of the second TV in the bedroom. I don't have a second TV in my unit, and I don't see the termination of those cables back there in that cabinet, so I don't know precisely where mine are. But if you happen to have the second TV, I'll bet you find that video and audio connection connected to a Component/AV In connection there as well.
As I said, the box as delivered in non-functional. The actual input to the front TV (besides the cable connection from the antenna) from the DVD "Theater" unit is by HDMI cable running from the "HDMI Out" connection on the DVD directly to the "1 HDMI In" connection on the TV; I assume (but don't know) that if a bedroom TV is installed, a second HDMI cable runs from the DVD to that as well to play DVD's.
Since the box is not used as delivered, I simply unplugged the 12-volt connection on mine so it wouldn't stay powered up. If I need an additional input to my TV at some point, I can re-power the box and plug in whatever I'm going to use to the box input.
All the best, Mike