A computing system or computer system consists of the computing device and then peripherals.
Computer is the basic computing device which is inside the PC/desktop. It includes the main processor with co-processors. It also consists of RAM, EPROM, input and output Ports, ports for networking and communications, graphics processors etc.. ALU (arithmetic and logic unit) is a part of the computer.
Peripherals are the additional (external or internal) devices that make the computer useful to users. Keyboard, mouse, display screen monitor, joystick, USB controller for flash pen etc, hard disk drive (controller), DVD drive (or controller) are examples of peripherals. A tablet, printer or any useful device like scanner special electronic device are all peripherals.
The processor initializes the peripherals connected to it, when it is switched on. The data from the input peripheral devices is read by the processor when needed and then data/text/pictures are sent to the output devices after computations are done.
Without the peripheral devices, a computer system is not useful to any one. In order that a peripheral works properly with the computer, a special software called driver software must be already present inside the operating system software.