1. Broadly, the system software stored in a computer's read-only memory (ROM) or elsewhere in the computer's circuitry, such as the basic input-output system (BIOS) chips in IBM PC-compatible computers. From QUECID

2. /ferm'weir/ n. Embedded software contained in EPROM or flash memory. It isn't quite hardware, but at least doesn't have to be loaded from a disk like regular software. Hacker usage differs from straight techspeak in that hackers don't normally apply it to stuff that you can't possibly get at, such as the program that runs a pocket calculator. Instead, it implies that the firmware could be changed, even if doing so would mean opening a box and plugging in a new chip. A computer's BIOS is the classic example, although nowadays there is firmware in disk controllers, modems, video cards and even CD-ROM drives. From Jargon Dictionary

3. Programming that is inserted into programmable read-only memory (PROM), thus becoming a permanent part of a computing device. Firmware is created and tested like software (using microcode simulation). When ready, it can be distributed like other software and, using a special user interface, installed in the programmable read-only memory by the user. Firmware is sometimes distributed for printers, modems, and other computer devices. From Linux Guide @FirstLinux