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When a multitasking operating system stops running one process and starts running another. Many operating systems implement concurrency by maintaining separate environments or "contexts" for each process. The amount of separation between processes, and the amount of information in a context, depends on the operating system but generally the OS should prevent processes interfering with each other, e.g. by modifying each other's memory.
A context switch can be as simple as changing the value of the program counter and stack pointer or it might involve resetting the MMU to make a different set of memory pages available.
In order to present the user with an impression of parallism, and to allow processes to respond quickly to external events, many systems will context switch tens or hundreds of times per second.