I have a question about TiVo?

I understand it's a dvr let's call it, I have dish network but I recently moved and didn't have the 3rd single recover installed because it would of cost 399$ and cords would be all over the place, so I am wondering if I can hook TiVo up to my dish network dvr and likes save my current recordings on the living room tv then bring the TiVo box into my bedroom and watch them, I may sound really dumb, but I really don't have a clue about what TiVo REALLY is.. Help me, please?