RTOS Is a powerful program generally written in c or c++ programming languages for the micro controllers to perform the actions in real time .Real time means action and reaction of the system on time as expected. Like Airbags in the cars.If not performed action on time the passenger or driver may die. So if you think on the higher level where we need real time action or reaction .It all depends on the application you are building .For example In industries there are lot of machines which needs to be synchronized together to do the final work. These machines are highly time critical and the micro-controllers which are driving them must be using RTOS in it. There are industries which deals with the electro-mechanical and highly safety critical systems.Like Avionics ,Nuclear ,Automotive ,Medical they all need to use RTOS to get the high responsiveness from their systems.
Their are various kinds of RTOS available in the market but all are not exactly same. They all have their own features ,price and support to the customer and can be selected according to the need of the product. For more information checkout this course on RTOS development.