The computer device that works like the human central nervous system is the Motherboard. This is such in that it is the central most part of the system and connects everything together.
The motherboard is the main PCB (Printed Circuit Board) that exists inside most PC's, and in certain other systems. The function of the motherboard is to contain most of the essential components to a functioning system. This includes the CPU (central processing unit) and storage of memory. There are various different components that comprise the Motherboard.
The clue here is in the terminology! The term Motherboard is derived from the fact that it is quite literally the 'mother' of the computer system. It is the central most part of the system and it connects all parts together, including networks, storages and hard drives.
I hope this answers your question.