What happens and what is the danger to your computer if the CMOS battery dies?
The CMOS battery is a very low powered device, just like a little watch battery.
So don't stress, it ain't gonna kill you.
However, its needed to keep data in the CMOS. The CMOS tells the computer what processor is installed (although many computers have jumpers set to tell it this), what drives you have (diskette, hard disk, CD-ROM, and others, and importantly your hard drive's geometry), how much memory is installed, and other important data that your computer needs to know in order to run correctly....
I imagine what would happen if it completely ran out would be that the CMOS would have to be re-written to manually in your BIOS program every time the machine was powered on for anything like normal operating to occur. Certainly you would loose the time settings and would have to redirect the BIOS to redetect the hard drives everytime you powered on.
You can replace a CMOS battery quickly and easily. They are very cheap and just clip out and in to the motherboard. It resembles a small silver disc about the size of a coin.
This is assuming that your computer is not totally ancient (like a 8088, 8086, maybe 286 or something) where the CMOS battery was sometimes not removable. If this is the case then get a new computer you sad man..... Otherwise, it will cost you nothing to replace and if you are not sure of yourself a computer store will do it in about 1 minute.