An input-output processor (IOP) handles input/output (I/O) tasks by directly accessing and storing data in memory without involving the CPU. It acts as an interface between the computer and I/O devices. When an I/O device needs to access or store data in memory, it requests the DMA controller, which sends a hold request to the CPU. The CPU acknowledges and the DMA controller allows for direct data transfer between the I/O device and memory without CPU involvement. This speeds up I/O tasks and reduces CPU overhead.