Your brain is an energy-hungry organ - even when you're resting, it can use up to 25% of available energy (chimp brains use about 8%: Gibbons, 2007). In other words, the running costs of a large brain are quite high. And yet humans, with their large brains, take in about the same number of calories as similar-sized but smaller-brained mammals. How can this be?
The usual explanation is a shift in diet and the related downsizing of our guts. Humans eat more meat than other apes, and meat provides more, & more easily-accessed, calories than plant material. This means that carnivores & omnivores don't need to process food as much as herbivores, or for as long, to get the same amount of energy & nutrients from it. And they have shorter guts. Ann Gibbons (2007) reports that this hypothesis has been extended by the suggestion that it was cooking that allowed development of a longer brain, because it effectively predigests food and further reduces the amount of energy used by the body in processing nutrients - freeing that energy up for other things.
While not everyone agrees that cooking triggered an expansion in brain size, certainly something must have happened to early humans' energy budgets. As Gibbons notes, brain size increased three-fold between the earliest appearance of Homo erectus (ergaster) - which itself has a brain markedly larger than the australopiths - and the evolution of the sister species sapiens & neandertalensis. And there's a lot of evidence to suggest that this is linked to meat-eating. For example, while earlier hominins may have scavenged meat here & there, we know that erectus systematically butchered and processed carcasses. But the cooking?
Supporters of the cooking hypothesis note that, at the same time, erectus's teeth were getting smaller - in comparison, as other mammals have moved to carnivory they've tended to evolve larger teeth. It's argued that this is evidence that erectus was not only a hunter, but also a chef: cooked food is softer & easier to chew, so there'd be no selection pressure driving evolution of larger teeth. And experiments have shown that it takes less energy (& time) to digest cooked meat - leaving more energy for other activities.
The crunch comes when you look for direct evidence of cooking: hearths, charred bones, & so on. Perhaps the earliest evidence of controlled use of fire date back 790,000 years, in Israel. That's much later than the timing of brain expansion in erectus. Consequently not everyone accepts the idea of an erectus version of Jamie Oliver, suggesting instead that systematic cooking of food is an innovation associated with the appearance of the particularly big-brained Neandertals & sapiens around 200,000 years ago. So meat-eating definitely shaped our evolution, but the jury's still out on the timing & impact of the culinary arts.
A. Gibbons (2007) Food for thought. Science 316: 1558-1560