Your computer stops what it is doing and follows your demands. While it does this, it is also handling IRQs from your mouse and various cards. It can handle thousands of IRQs per second. This is an IRQ line. Each part must have its own IRQ line, so if you set two pieces of hardware to the same IRQ line, your computer will have an IRQ conflict and more than likely one of the pieces of hardware involved in the conflict will not work.
Some people make an art of jiggling IRQs around in their systems.
This one concept is the basis of many headaches involved with installing new expansion cards. When your CPU responds to an IRQ, it usually sends data back to the part that asked for it. Often, the card will ask for the same data again and again, so to save the CPU the time of re-thinking the information and sending it over, DMA, or direct memory access, was invented. DMA is usually composed of a message sent to the card saying where to look in the memory for the data. This makes things faster.