Computer software can be categorized into system software and application software. System software includes the operating system and system utilities, with the operating system responsible for starting the computer, managing applications and memory, handling input/output, and providing the user interface. System utilities are used for maintenance tasks like managing disks, printers, and devices to keep the system running smoothly. Application software enables users to perform a variety of tasks through programs like word processing, spreadsheets, presentations, databases, and web browsers.