The arrival of an interrupt request from an external device causes the processor to suspend the execution of one program and starts the execution of another. The execution of this another program is nothing but the interrupt service routine for that specified device.
Interrupt may arrive at any time. So during the execution of an interrupt service routine, another interrupt may arrive. This kind of interrupts are known as nesting of interrupt.
Whether interrupt nesting is allowed or not? This is a design issue. Generally nesting of interrupt is allowed, but with some restrictions. The common notion is that a high priority device may interrupt a low priority device, but not the vice-versa.
To accomodate such type of restrictions, all computer provide the programmer with the ability to enable and disable such interruptions at various time during program execution. The processor provides some instructions to enable the interrupt and disable the interrupt. If interrupt is disabled, the CPU will not respond to any interrupt signal.
On the other hand, when multiple lines are used for interrupt and priorities are assigned to these lines, then the interrupt received in a low priority line will not be served if an interrupt routine is in execution for a high priority device. After completion of the interrupt service routine of high priority devices, processor will respond to the interrupt request of low priority devices