what is the CPU in computers and desktops

The central processing unit (CPU) of a computer is a piece of hardware that carries out the instructions of a computer program. The CPU is the brains of the computer - every instruction, no matter how simple, has to go through the CPU.  When you use a computer you want the instructions to be carried out very fast. As the instructions become more complicated (for example, creating a 3D animation or editing a video file), we demand more from the CPU.

Components

A typical CPU has a number of components. First is the arithmetic logic unit (ALU) which performs simple arithmetic and logical operations. Second is the control unit (CU) which manages the various components of the computer. It reads and interprets instructions from memory and transforms them into a series of signals to activate other parts of the computer. The control unit calls upon the arithmetic logic unit to perform the necessary calculations. Third is the cache, which serves as high-speed memory where instructions can be copied to and retrieved. Early CPUs consisted of many separate components, but since the 1970s they have been constructed as a single integrated unit called a microprocessor. As such, a CPU is a specific type of microprocessor. The individual components of a CPU have become so integrated that you can't even recognize them from the outside. The CPU shown below is about 2 inches by 2 inches in size.

CPUs are located on the motherboard. Motherboards have a socket for this, which is specific for a certain type of processor. A CPU gets very hot and therefore needs its own cooling system in the form of a heatsink and/or fan.