Stands for "Interrupt Request." PCs use interrupt requests to manage various hardware operations. Devices such as sound cards, modems, and keyboards can all send interrupt requests to the processor. For example, when the modem needs to run a process, it sends an interrupt request to the CPU saying, "Hey, hold up, let me do my thing!" The CPU then interrupts its current job to let the modem run its process.
It is important to assign different IRQ addresses to different hardware devices is because the interrupt request signals run along single IRQ lines to a controller. This interrupt controller assigns priorities to incoming IRQs and sends them to the CPU. It's kind of like taking a number at the local deli, except the hardware usually only has to wait a couple of nanoseconds instead of like twenty minutes). Since the interrupt controller can control only one device per IRQ line, if you assign the same IRQ address to multiple devices, you are likely to get an IRQ conflict. This can cause a range of errors from not allowing network connections to crashing your computer. So make sure you assign unique IRQs to new hardware you install and avoid the frustration and keyboard throwing that conflicts can cause.