Software is categorized into two types: system software and application software. System software includes operating systems and manages the interaction between hardware and other software. It is low-level, fast, and difficult to design and understand. Application software satisfies specific needs like word processing, spreadsheets, and payroll. It is higher-level, easier to design and use, and allows for more interaction than system software. Examples of application software include Microsoft Office, inventory management software, and student records systems.