BIOS is an acronym, short for Basic Input Output System.
It's what your system uses to "get smarter." BIOS is the first thing your computer runs, and it's stored on the computer's motherboard. It runs just enough information to access the disk, and it tells the computer how to read the hard drive. Then the disk can go out and recognize all the components of your computer-- the video card first, so you can see what's happening on your monitor, then the rest of your hardware, and so on.
Note: BIOS is not what people are referring to when they say "change your BIOS." They are talking about the Setup Program in BIOS that modifies the CMOS, where all your non-volatile memory (date, time, and so on) is stored.