A Programmable Interrupt Controller (PIC) is a device which allows priority levels to be assigned to its interrupt outputs. When the device has multiple interrupt outputs to assert, it will assert them in the order of their relative priority. Common modes of a PIC include hard priorities, rotating priorities, and cascading priorities. PICs often allow the cascading of their outputs to inputs between each other.
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Well-known PICs
One of the best known PICs, the 8259A, was included in the x86 PC. In modern times, this is not included as a separate chip in an x86 PC. Rather, its function is included as part of the motherboard's southbridge chipset. In other cases, it has been completely replaced by the newer Advanced Programmable Interrupt Controllers which support many more interrupt outputs and more flexible priority schemas.
More Information
More information on the Intel APIC can be found in the IA-32 Intel Architecture Software Developer's Manual, Volume 3A: System Programming Guide, Part 1, Chapter 8, freely available on the Intel website.