Firmware is software that is stored in a chip inside the LiteOn (or any other burner, cdrom, dvdrom, HD, etc)
This software basically controls the fundermental way the unit works (similar to the BIOS in your computer's motherboard) and as with any bit of software, it can have bugs or shortcomings. When a problem/bug is found, they fix it, re-issue the firmware as an installable file (well LiteOn does, others do not) that basically overwrites the existing software with the new one.
Some people upgrade their Firmware as new versions are issued for their equipment without knowing what the differencs to older versions are. They assume the latest is the greatest (not always true!) Others take the attitude, if it aint broke, dont fix. Unless you are having some real problems with your unit, the latter option is allways the best.