What is the brain in the computer?

The "brain" would be called the CPU or Central Processing Unit - now known as a Microprocessor. However, the Microprocessor requires both the motherboard and memory to function. If you want to know how it relates to the human brain - all three form the "brain". The microprocessor contains all of the hardware (i.e. transistors) to execute a sequence of instructions provided by a software program. The motherboard connects everything together and contains basic software.

From there, you have storage in the form of hard drives, user interfaces are monitors, keyboards, and a mouse, other peripherals are cd/dvd drives, USB devices, sound cards, modems, etc.

A google search for CPU will yield a wikipedia result that goes into more detail on the CPU.
Central processing unit - CPU