Best I can tell, the fracas began when Google discovered that someone in China had attacked their systems/servers. It sounds as though Adobe, Yahoo, and a number of other American companies may also have been attacked.
The possible goals of the Chinese cyberattack:
- Obtaining commercial/proprietary information.
- Inserting spyware into Google's system.
- Breaking into the gmail accounts of Chinese dissidents and American experts on China
The articles I've read do not make it clear whether Google thinks the breach was orchestrated by the Chinese government or was a private operation.
As far as the reason that China does not like Google (and/or vice versa), there'd been a dispute about "Chinese pressure on it to make sure Chinese users could not directly link to the American-based google.com site, to evade much of the censorship the company had reluctantly imposed on its main Chinese portal, google.cn."