I believe it stands for Interrupt Request. Basically an external device sends a signal to it's IRQ to request that the CPU temporarily interrupt it's current process so that the device can send or recieve information to be processed.
There are 16 IRQs; but 4 are used for the internal system, 3 for the normal filesystems (1 floppy, and 2 IDE ports), 2 for the keyboard and mouse (unless using USB devices), 1 or 2 for the sound card, 1 for the graphics card, 1 for each USB root, 1 for each serial port, 1 for each parallel port (though as mentioned they may not be used), etc...