A time-sharing operating system allows multiple users to access a computer system simultaneously. It divides the CPU's time among various tasks, giving the illusion that each user has their own dedicated machine. This is achieved through rapid switching between tasks, enabling efficient resource utilization and improved response times. These systems are designed to manage multiple processes and ensure fair access to resources. By using techniques like multitasking and scheduling algorithms, time-sharing operating systems enhance user experience and productivity. Examples include Unix and Linux, which support multiple users and processes effectively.