Importance:

1.  It is a master's program that controls the computer system.
2. It acts as an intermediary between the user and the computer hardware.
3. It porvides an environment in which a user can execute other application programs in a convenient and effiecient manner.
4.  It hides the complexities of the hardware from the user.
5.  It manages the hardware resources in order to provide for an orderly controlled allocation of the processors, memorises, and I/O devices among the various programs competing for them.  

Operating system can be classified into following categories: 

1.  Multiprogramming OS: Multiprogramming OS is an ability of an operating system that executes more than one program using a single processor machine. More than one task or program or jobs are present inside the main memory at one point of time.
2.  Mulitasking OS: multitasking is the concurrent execution of multiple tasks over a certain period of time. New tasks can interrupt already started ones before they finish, instead of waiting for them to end.
3.  Multiprocessing OS: A multiprocessing operating system (OS) is one in which two or more central processing units (CPUs) control the functions of the computer.The use of multiple processors allows the computer to perform calculations faster, since tasks can be divided up between processors.
4.  Distributed OS: A distributed operating system is system software over a collection of independent, networked, communicating, and physically separate computational nodes. They handle jobs which are serviced by multiple CPUs. Each individual node holds a specific software subset of the global aggregate operating system.
5. Network OS: A network operating system is a specialized operating system for a network device such as a router, switch or firewall. sharing 
6. Time sharing system: Time-sharing is a technique which enables many people, located at various terminals, to use a particular computer system at the same time. Time-sharing or multitasking is a logical extension of multiprogramming. Processor's time which is shared among multiple users simultaneously is termed as time-sharing.
7.  Multithreading OS: Multithreading is the ability of a program or an operating system process to manage its use by more than one user at a time and to even manage multiple requests by the same user without having to have multiple copies of the programming running in the computer.
8. Batch processing OS: Batch processing is a technique in which an Operating System collects the programs and data together in a batch before processing starts.