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Operating systems have two primary functions: they run (and schedule) applications and they give users access to resources. When a program starts, the operating system must allocate memory to a "process" in which it will operate. It must hand up control of the CPU to the process, and it does so in one of two ways. The first is when the program crashes or exits. The second method is to use a multi-tasking system to schedule tasks.
Most, but not all, operating systems are multitasking, but this is a very new phenomenon. There are multiple processes in an MT OS that are all "running" at the same time. Only one of these, though, has the CPU really running its code. When a timer runs out, the operating system records everything the running process did before handing the CPU over to another process. It strives to do so in a way that is equitable to all "running" processes, such that everyone advances.
When dealing with modern systems with two, four, or even eight cores, the task becomes even more difficult. Now the scheduler must cope with scheduling each of those CPUs, while also taking into account the fact that moving a process from one to the other may result in a performance hit due to cache behavior.
Another thing an OS does is provide you access to things like hard disks, optical drives, USB devices, graphics cards, monitors, and even things like turning on the fans. Programs are usually constructed in such a way that the programmer doesn't have to worry about where a file is read or written from. All of this is managed by the operating system, which provides a common interface for many types, models, and brands of hard drives, as well as various types of mice, keyboards, microphones, speakers, and headsets. Because the OS provides a standard mechanism to interact with them, programs (and hence programmers) don't have to worry about it.
Samsung and Frost & Sullivan recently conducted a survey of 500 managers and executives from enterprises and government organizations in the United States to learn more about how they use mobile devices and applications in the workplace. The results are astounding: Respondents report gaining nearly an hour (58 minutes) of work time per day and nearly an hour (58 minutes) of leisure time per day as a result of utilizing cellphones to get work done, resulting in a 34 percent improvement in productivity. The minutes gained are slightly higher for very large businesses, but the efficiency gains are greatest for mid-sized businesses. In any case, that's a lot of quantifiable worth.