The 8259 Programmable Interrupt Controller (PIC) handles multiple interrupt requests from I/O devices connected to the CPU. It has 8 interrupt lines and can prioritize and process interrupts. It includes registers to store interrupt requests and service status, and can cascade with other PICs to handle more interrupts. When an interrupt occurs, the PIC sends a call instruction to the CPU, then the interrupt service routine address, allowing the CPU to service high-priority interrupts first in a multitasking system.