These first two quotes are straightforward explanations of what an operating system actually is. Things are, however, more complex than that.
An operating system (OS) is a computer program that manages the hardware and software resources of a computer. At the foundation of all system software, the OS performs basic tasks such as controlling and allocating memory, prioritizing system requests, controlling input and output devices, facilitating networking, and managing files. It also may provide a graphical user interface for higher level functions.
Wikipedia
Your computer, despite being a collection of highly sophisticated parts, is really just … well, a collection of highly sophisticated parts. On its own, it can do nothing other than switch on and off and spin a disc or two. In order for it to do anything useful, it needs an operating system (OS) to guide it. The OS takes an essentially well-endowed but completely uneducated hunk of a machine and educates it, at least enough so that it will understand what you want it to do. < ?php amm_getMediaID('amm_default_output',29);?>