embedded software which runs on a device such as a camera/lens, phone, or computer
Firmware is the software which controls a camera's functions.
Manufactures often update the firmware to fix problems, or add new features. General instructions for updating firmware are here - http://photo.stackexchange.com/questions/13266/should-i-worry-about-the-firmware-version-on-my-dslr-and-if-so-how-do-i-update - and here - http://photo.stackexchange.com/questions/15759/where-can-i-find-firmware-updates-for-nikon-and-how-do-i-install-them
Firmware can be "hacked" (modified by 3rd parties other than the manufacturer) to add functionality. Well known modifications are CHDK and Magic Lantern for Canon. There is a less successful project for Nikon - Nikon Hacker Project
For further information on firmware hacking: