There are several explanations for this: meat and sociality among them. These are of course not mutually exclusive, by the way. There are a couple of papers by Ann Gibbons (here, here) in the latest Science issue that discuss new evidence and the controversies surrounding the role of cooking meat in allowing for increased energy allocation to brain size.
To find support for his ideas, Wrangham went to the lab to quantify the nutritional impact of cooking. He found almost nothing in food science literature and began to collaborate with physiologist Stephen Secor of the University of Alabama, Tuscaloosa, who studies digestive physiology and metabolism in amphibians and reptiles. Secor's team fed 24 Burmese pythons one of four diets consisting of the same number of calories of beef: cooked ground beef, cooked intact beef, raw ground beef, or raw intact beef. Then they estimated the energy the snakes consumed before, during, and after they digested the meat, by measuring the declining oxygen content in their metabolic chambers. Pythons fed cooked beef spent 12.7% less energy digesting it and 23.4% less energy if the meat was both cooked and ground. "By eating cooked meat, less energy is expended on digestion; therefore, more energy can be used for other activities and growth," says Secor. Secor also helped Wrangham and graduate student Rachel Carmody design a pilot study in which they found that mice raised on cooked meat gained 29% more weight than mice fed raw meat over 5 weeks. The mice eating cooked food were also 4% longer on average, according to preliminary results. Mice that ate raw chow weighed less even though they consumed more calories than those fed cooked food. "The energetic consequences of eating cooked meat are very high," says Wrangham.
But, there is the issue of when hominins (H. erectus) were first able to use fire. The best evidence for human use of fire happens quite long after the burst in brain size that happened about 2 million years ago.the last paragraph:
Others, such as Carel van Schaik of the University of Zurich, think that cooking may have played an important role early on, along with other adaptations to expand human brainpower. As Aiello observes, the big brain was apparently the lucky accident of several converging factors that accentuate each other in a feedback loop. Critical sources of energy to fuel the brain came from several sources--more meat, reduced guts, cooking, and perhaps more efficient upright walking and running. The order in which our ancestors adopted these energy-saving adaptations is under hot debate, with the timing for cooking hardest to test. Regardless, "it's all beginning to come together," says Aiello.