Interrupts play a crucial role in improving the efficiency of a computer system. By allowing devices and software to request attention only when necessary, interrupts help reduce wasted processing time and improve overall system responsiveness. Without interrupts, the processor would have to continuously poll devices and software for updates, resulting in inefficient use of system resources. Interrupts enable the processor to perform other tasks while waiting for a device or software to finish its operation, maximizing the utilization of system resources and enhancing system performance.