Computer architecture involves understanding how hardware components like the CPU, memory, and input/output devices work together to execute instructions and store/retrieve data. The CPU fetches instructions from memory and controls data flow, while the arithmetic logic unit performs calculations. Memory stores instructions and data for the CPU and comes in volatile forms like RAM or non-volatile forms like ROM. The motherboard contains these core components and provides connections for other peripherals like storage devices, graphics cards, and input/output devices.