The OS is responsible for everything from enabling hardware components to function (components like modems, printers and monitors) to how to communicate with the Internet as well as playing the role of traffic cop for all of the software.
The OS allocates the resources of the PC to the software and hardware in an organized way. The resources include things like memory storage space, access to the hard disk and what is displayed on the monitor. Without the OS, the software programs might interfere with each other, causing the PC to malfunction or crash continually. Even with the OS, many PCs have difficulty operating smoothly. That illustrates just how complicated the tasks of an OS actually are.
While the OS is technically a software program, it is distinct from other software specifically referred to as "application software". Application software, we'll just call it software, are programs that you install onto a PC that make the PC useful.
Software is a complex series of instructions telling the computer what to do. The instructions are very detailed because they have to tell the computer every single step to be performed. For example a word processing program has instructions for what to do when you press the letter "A". The software tells the computer to take the letters as they are pressed on the keyboard, then it tells it to add the letter to the letters you already typed and it tells the computer to display the letter on the screen so you can see what you have typed. The computer doesn't do anything without very explicit instructions.