Firmware is a term sometimes used to denote the fixed, usually rather small, programs that internally control various electronic devices. Typical examples range from end-user products such as remote controls or calculators, through computer parts and devices like harddisks, keyboards, TFT screens or memory cards, all the way to scientific instrumentation and industrial robotics. Also more complex consumer devices, such as mobile phones, digital cameras, synthesizers, etc., contain firmware to enable the device's basic operation as well as implementing higher level functions.
Naturally, there is no strict, or well defined, boundaries between firmware and software, both are quite loose descriptive terms. However, firmware is typically involved with very basic low-level operations in a device, without which the device would be completely non-functional. Firmware is also a relative term, as most embedded devices contain firmware at more than one level. Subsystems such as LCD modules, flash chips, communication controllers etc, have their own (usually fixed) program code and/or microcode, regarded as 'part of the hardware' by the higher level firmware.
Simple firmware typically reside in ROM or OTP/PROM, while more complex firmware often employ flash memory to allow for updates. Common reasons for updating firmware include fixing bugs or adding features to the device. Doing so usually involves loading a binary image file provided by the manufacturer into the device, according to a specific procedure; this is sometimes intended to be done by the end user.