According to lead researcher Verena Seufert at McGill University, the reason for the difference in yields centers on nitrogen usage and irrigation. Conventional crops received large doses of nitrogen from chemical fertilizers while organic crops rely on manure, compost, and cover crops which provide smaller amounts of nitrogen.
Seufert suggests that perhaps there is a "hybrid" system that could be developed to increase yields but still support organic production. This article does not review this in any detail only suggesting that it could be developed "utilizing management practices from both systems."
For more see:
Meyer, Bob. "Can organic production feed the world?" Brownfield Ag News, 27 April 2012.
Seufert, Verena, Navin Ramankutty, and Jonathan A. Folley, "Comparing the yields of organic and conventional agriculture," Nature, 25 April 2012.