As an example: Building Bare-Metal ARM Systems with GNU
Many embedded systems do not have enough resources for a full OS, some may use a scheduler kernel or RTOS, others are coded 'bare metal'. The main() C entry point is entered after reset. Only a small amount of assembler code is required to initialise a microprocessor, to execute C code. All C requires to run generally is a stack - usually simply a case of initialising the stack pointer to a specific address. Some processor specific initialisation of interrupt/exception vectors, system clocks, memory controllers etc. may be necessary also.
On a desktop PC, typically you have a BIOS that handles basic hardware initialisation such as SDRAM controller setup and timing, and then bootstrapping from a disk boot-sector, which then in turn bootstraps an OS. Any of that code could be written in C (and some of it probably is), and it could do something other than boot an OS - it could do anything - it is just code.
OSs are useful for non-dedicated computing devices where the end user many select one of many programs to execute and possibly several simultaneously. Most embedded systems do just one thing, the software is often loaded from ROM or executes directly from ROM, and is never changed and executes indefinitely (usually stopped only by power-down).
You still of course might implement device drivers and the like, but often these are an integral part of the application rather than a separate entity. Even when you do use an RTOS in an embedded system, it is still generally integral to your application rather than an OS in the sense you might understand. In these cases the RTOS is simply a library like any other, and is often initialised and started from main() rather then the other way around as you might expect.