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 - Should I worry about the firmware version on my DSLR, and if so, how do I update? - and here - 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 succesful project for Nikon - Nikon Hacker Project
For further information on firmware hacking: