What is difference between interupt and subroutine?

Interrupt is the signal generated by the input/output devices in order to take the attention of the processor.

When the processor receives the interrupt signals it checks the priority status and finish the current fetch and execute cycle and (if the priority status is high) allow the input/output device to process their tasks. Then previous fetch and execute cycle is continued. This is called interrupt service routine.

The programs are broken down in to small sub programs which are called subroutines. Then the program reusability, readability, maintainability ...etc will be increased.