an embedded operating system
An embedded operating system is the software running inside a device that is not thought of as a computer at all — a microwave, a thermostat, a smartwatch, a drone, a sensor in a factory, a key fob. The computer is embedded inside a larger product to do one focused job. Picture the brain of a calculator versus the brain of a laptop: the calculator's needs are narrow and fixed, so its OS can be tiny, frugal, and tailored exactly to the task, rather than a big general-purpose system trying to do everything.
The defining constraints are footprint and resources. Such systems often have only kilobytes to a few megabytes of memory, a slow low-power processor, no disk, and sometimes no screen, so the OS must be very small and lean. Many embedded operating systems ship as a single library you link directly with your application, with no separation between user mode and kernel mode and no virtual memory at all, because the hardware may lack a memory management unit. Many are also real-time, since the device must react to physical events on time. The Internet of Things (IoT) — billions of small connected gadgets — has made this category huge, and added the hard problem of keeping such tiny, long-lived, hard-to-update devices secure.
An honest clarification is that embedded and real-time overlap but are not the same idea. Embedded is about where and how small the system is (inside a constrained device); real-time is about timing guarantees. Many embedded systems are also real-time, but a simple embedded gadget with no hard deadlines is still embedded, and a real-time system could in principle run on big hardware. The shared theme is doing more with very little, and being trusted to run unattended for years.
A smart thermostat may have just 256 KB of RAM and no disk. Its embedded OS is linked together with the application into one small image that boots in a fraction of a second, reads the temperature sensor, drives the display, talks to Wi-Fi, and does nothing else — there is no room or need for a full desktop operating system.
One focused job, tiny memory: the OS is shrunk to fit the device.
Embedded does not automatically mean real-time, and vice versa. Embedded is about being small and built into a device; real-time is about guaranteed timing. Many devices are both, but the two properties are separate.