The operating system is, simply, what empowers your software to manage the hardware. Clearly some OSes are more sophisticated than others.
At its very core, a computer starts executing at a fixed address, meaning that when the computer starts up, it sets the program counter to a pre-defined address, and just starts executing machine code.
In most computers, this "bootstrapping" process immediately initializes known peripherals (like, say, a disk drive). Once initialized, the bootstrap process will use some predefined sequence to leverage those peripherals. Using the disk driver again, the process might read code from the first sector of the hard drive, place it in a know space within RAM, and then jump to that address.
These predefined sequence (the start of the CPU, the loading of the disk) allows the programmers to star adding more and more code at the early parts of the CPU startup, which over time can, eventually, start up very sophisticated programs.
In the modern world, with sophisticated peripherals, advanced CPU architectures, and vast, vast resources (GBs or RAM, TB of Disk, and very fast CPUs), the operating system can support quite powerful abstractions for the developer (multiple processes, virtual memory, loadable drivers, etc.).
But for a simple system, with constrained resourced, you don't really need a whole lot for an "OS".
As a simple example, many small controller computers have very small "OS"es, and some may simply be considered a "monitor", offering little more than easy access to a serial port (or a terminal, or LCD display). Certainly, there's not a lot of needs for a large OS in these conditions.
But also consider something like a classic Forth system. Here, you have a system with an "OS", that gives you disk I/O, console I/O, memory management, plus the actual programming language as well as an assembler, and this fits in less than 8K of memory on an 8-Bit machine.
or the old days of CP/M with its BIOS and BDOS.
CP/M is a good example of where a simple OS works well as a abstraction layer to allow portable programs to run on a vast array of hardware, but even then the system took less than 8K of RAM to start up and run.
A far cry from the MBs of memory used by modern OSes. But, to be fair, we HAVE MBs of memory, and our lives are MUCH MUCH simpler (mostly), and far more functional, because of it.
Writing an OS is fun because it's interesting to make the HARDWARE print "Hello World" shoving data 1 byte at a time out some obscure I/O port, or stuffing it in to some magic memory address.
Get a x86 emulator and party down getting a boot sector to say your name. It's a giggly treat.