to stop you getting spoilers from the Wiki page, this seems the best description:
The Hybrid
The Basestar’s internal functions are controlled by a part-biological, part-machine central computer system known as the Hybrid. The biological part of the Hybrid is a female humanoid Cylon-like being, housed inside an immersion tank similar to a Cylon re-birthing tank and attached to the mechanical part of the Basestar computers by umbilicals.[7] The Hybrids do not have a completely human body, but rather appear to be more like cyborgs, consisting of conduits and other connectors mated to, or in place of elements of their bodies. The Hybrid is not one of the “twelve models” of humanoid Cylon, but is a separate model that is essentially another stage in “evolution” from fully mechanical Centurion, to partially biomechanical Raider, to humanoid Cylon. Hybrids are similar to the autonomous biomechanical pilots within Raiders, specially constructed as living computers that manage the autonomic functions of the Basestar, including navigation and FTL jumps, climate control, and the like. The Hybrids are so integrated into the Basestar’s functionality that they are, for all practical purposes, the Basestar.
Basically in the scheme of Battlestar Galatica story line, don’t worry about em…