http://www.cnn.com/2015/01/01/us/mar...html?hpt=hp_t1
He was considered a possible future President, but then was upset in the 1994 gubernatorial race, where many Republicans notched surprise victories.
He also could have been appointed to the Supreme Court in 1993, but turned it down.
Cuomo was fairly liberal, strongly opposing the death penalty and was a huge proponent of affirmative action. Both of these stances hurt him in 1994, when there was a backlash against Democrats for being soft on crime (the early 90s saw an all-time high in US crime), as well as growing dissatisfaction with affirmative action policies.
His son Andrew is currently governor of New York.