Execution of a program in CPU is completed employing different set of registers and their individual circuitry. As CPU registers are used for execution of interrupt service routine also it's highly likely that these routines change the content of various registers. So it's the responsibility of operating system that before an interrupt service routine is executed previous content of CPU registers must be stored such that execution of interrupted program can be restarted without any change from point of interruption.  Hence at the beginning of interrupt processing necessary context of processor is saved either into a special save area in main memory or in a stack. This context is restored when interrupt service routine is completed, So interrupted program execution can be restarted from point of interruption.