A real-time operating system (RTOS) provides services, which helps to manage the continuously rising complexity of software development in embedded systems. In comparison to an operating system (OS) like Linux or Windows, the RTOS provides:
Deterministic and highspeed event handling
A scheduler which is able to meet timing deadlines
Usable from tiny microcontrollers to big processors
Note: When discussing the fundamental properties of a real-time operating system, it is not about super fast timings (of course, they are super fast) – more important is the guarantee and determinism of achieving the timing deadlines.