Noun: In meteorology, bombogenesis is a word coined by the weather folk that is derived from the term cyclogenesis. Cyclogenesis is the formation of cyclonic conditions, marked by a drop in atmospheric pressure, responsible for everything from hurricanes to tornadoes to blizzards.
Bombogenesis is simply cyclogenesis that forms very rapidly and abruptly. To use the meteorological jargon, bombogenesis occurs when there is "a central pressure drop of at least 24 millibars in 24 hours." The result is a particularly sudden, powerful, and "explosive" storm, hence the "bomb" in the word. A specific example of a tropical cyclone that underwent bombogenesis was Hurricane Charley in 2004. Typhoon Nuri in 2014 was another. Nuri, though it was thousands of miles away, is also the reason why those of us in the United States experienced some crazy weather in early November of 2014, with temperatures getting freakishly low throughout!
Other phrases used to describe this phenomenon are Explosive cyclogenesis, weather bomb, meterorological bomb, or explosive development, but I can see why they would prefer to use such a sensational, eye-catching word as bombogenesis. ^_^
Origin: Couldn't find the exact time it was first used, but I have my suspicions that it's modern. ;-)