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OS stands for Operating System not Operative System, and the "reformat your computer" was intended as a tongue-in-cheek answer. It's not the brain--that's the CPU--and it only controls the underlying layers, not everything. The user never really sees the OS, actually. When you are using Windows you are using a shell application that ships with the operating system, not the operating system itself.
The OS is the layer that sits between the program and the hardware. Originally its primary purpose was to manage the disk and file system, but the role of the OS has grown until now it manages nearly everything, including how memory is allocated and how pixels are drawn on your screen.
These days the most important thing the operating system does is coordinate the interactions between programs and eachother and programs and the computer. Long ago, if a program wanted to display anything on the screen it talked directly to the computer. If a program wanted to read information from the keyboard it would talk directly to the keyboard. If it wanted to print... you get the idea. But with modern operating systems that support many programs at once, this is no longer possible. When a program wants to draw on the screen or send data to the printer, it needs to coordinate with all the other applications. What if two programs try to print at the same time? You don't want the pages mixed. What if two programs want to draw at the same time? Or allocate memory at the same time? Or write to the hard drive at the same time? A big role of the operating system is managing these simultaneous requests.
This is in addition to the classical role of an operating system, which was to manage the file system. Where all that data is stored on the computer is a hugely complex problem. A file may be spread across hundreds of different locations on the hard drive, and could be scrambled and out of order. Since the first computers that had operating systems, the OS has managed the fine details of where the data was stored so all that logic didn't have to be reinvented each time a computer program was written.
Hope this helps.