Firmware is a program for computing device part inserted in PROM (programmable read-only memory). 
It is made through general process of software and tested by microcode simulation.
New firmware could be released on public and user can install it in PROM using special user interface (Firmware upgrade). 
Firmware is released for improvement of printer, modem or any other computing device (mp3 player).
IBM calls it microcode instead of firmware.