In embedded systems with hard real-time requirements, there are several ways to schedule tasks. Once the number of tasks you need to execute grows long enough, scheduling becomes a challenge. An RTOS is one way to manage these tasks with guaranteed, deterministic timing.

A concrete example: if you're in a car (an embedded system doing many things at once) and press the brakes, you want the car to be as responsive as possible. A real-time operating system will sacrifice other features of a general purpose OS to guarantee that the brakes are applied within a specified time interval after you press them.

Also, there are responses to a similar comment from when this was previously posted: https://news.ycombinator.com/item?id=32329499