Firmware is a software program that is coded in ROM (Read Only Memory) of a device , usually at time of manufacturing the device , We have generally firmware for smartphones , washing machines and other electronic devices.
Example of firmware UI (User Interface) used in camera is shown below :
Now , about "tomato" is a firmware particularly for routers , they are partially free and based on linux.Tomato firmware has good user interface which helps to monitor bandwidth usage in networks.
A screen from tomato firmware :
You can find wikipedia comparison on such firmwares here