Agree with most of these answers -- the key is in the relationships between Jiang Zemin and his cohort to the rest of the party.
Since stepping down as General Secretary (formerly the Chairman position), Jiang Zemin had been seen as a puppeteer within the party, pulling strings behind the scenes via the people he helped get to the top: Zhou Yongkang, Bo Xilai, et al.
Around 2010, as Hu Jintao and Wen Jiabao were preparing to transition out, the party was set to be torn apart internally, the tensions had grown so high around the questions of who would be Premier, appointed to the Central Committee, and so on. Jiang Zemin wanted his guys holding the keys to the kingdom. Hu and others within the party wanted Jiang's influence reduced.
Once Xi was finally chosen as General Secretary, the Party consolidated around him and, simultaneously, corruption was chosen as the way to go about eradicating the party of its factions. A few years later and here we are with multiple once-powerful officials booted from the CPC, in prison or elsewhere, on charges of which nearly any public official in China could be found guilty (most obviously Wen Jiabao) were they on the wrong side of the party.
The key point in all of this is that cracking down on corruption was a means of survival for the party. Not survival from a popular discontent, overthrow the government kind of threat, but rather from the party itself. Brilliant move for such an organization, and one that I can't imagine ever happening strategically in American politics, legal formality and the rest aside.