A Cylon rebirthing tank is a large tub where the consciousness of a deceased Cylon agent is transferred to a new Cylon body that is suspended within a thick gel. A blue light shines down onto the resurrected agent's head.
The tub apparently acts as a receiver from a Cylon download station (either planetary-based or via a Resurrection Ship) where the consciousness of a killed Cylon agent is re-integrated into a new body to begin life anew, and with the opportunity to continue their work for the Cylon collective. Other agents tend to the new body as its consciousness reforms, encouraging and comforting the recovered agent in a fashion that may be reminiscent to viewers as midwifery.
The copy of Number Six that plays a dominant role in the Fall of the Twelve Colonies is resurrected in the tank, as is the Galactica-stationed copy of Sharon "Boomer" Valerii (Downloaded).