You can think of firmware simply as "software for hardware." Devices that you might think of as strictly hardware such as optical drives, a network card, a router, or a scanner all have software that is programmed into special memory contained in the hardware itself.
Manufacturers of CD and DVD drives often release regular firmware updates to keep their hardware compatible with new media. Network router manufacturers often release updates to firmware on their devices to improve performance or add additional features.
Visit your hardware manufacturer's support website for more information on firmware updates.