These radio transmission are collected by civilian ADS-B receivers located in the vicinity of the aircraft.
These ADS-B receivers are only able to collect information on flights within radio-range of their position, so the data they collect is usually sent to a central server which aggregates feeds from numerous individual receivers throughout the world.
This application of flight tracking is currently in its infancy, but is set to grow significantly as systems get more connected.
Despite the progress, many abrupt events like sudden weather changes are not captured by existing flight trackers because they take their information not from the airplane itself but from dispatcher centers which often do not know the actual status of plane's whereabouts.
The type of software available also imports and reviews global weather and NOTAM information to monitor any emerging issues that could affect the flight.