In PCs, an IRQ is a signal from a piece of hardware (such as a keyboard or sound card) indicating that it needs the CPU to do something. The interrupt request signals run along the IRQ lines to an interrupt controller that assigns priorities to incoming IRQs and delivers them to the CPU. Since the interrupt controller expects signals from only one device per IRQ line, if you have more than one device sending IRQ signals along the same line, you get an IRQ conflict that can freeze your machine. This is why assigning IRQs to new hardware as you install it is so important--and why it can be such a pain when it goes wrong.
See also: Plug and Play