The word breaking in this context means to
undergo a change or enter a new state, in particular ... of news or a scandal [NOAD]
Etymonline has this interesting tidbit to offer about break:
Meaning "to disclose" is from mid-13c.
That meaning is the flip side of the way you used it, and it is a transitive verb: "He broke the news to me that .." I believe that got modified to "breaking news" by extension.