The Operating System is the main code that runs the computer. Some examples include Windows, Linux, and Mac OSX.
Operating systems are the program that runs your computer and other programs on top of it. The OS is responsible for handling system resources and managing disk and memory access, as well as timing and memory protection.
The main code of the OS is called the kernel. Most OSs today have a monolithic kernel, meaning that the main code and drivers are contained in the kernel. Another kernel is a micro-kernel, meaning that most of the drivers act outside of the kernel, and are accessed as servers. Minix is one example of such a kernel.