The social brain
With the brain size of monkeys, the potential size of the social group increases, as individuals with the larger brains can establish and maintain social relationships with a larger number of group members (Robin Dunbar).
The advantage of the larger social group and the advantage of greater contact ability lead to a selection of individuals and groups with the larger brains. Selection promotes brain growth, as confirmed by hominid fossils.
The brain is an expensive organ because it consumes a lot of energy that the living being has to provide. Why did it paid off in evolution to invest in large brains?
Robin Dunbar answers this question with the hypothesis of the social brain (social brain hypothesis), which I will present later, after his essay Why people became completely different:
The hypothesis of the social brain provides an explanation for the observation that considering their body size, primates in general have developed much larger brains than other groups of animals.
The underlying argument is that the explanation sought lies in the fact that primates have more complex social systems than other animal species and that this complexity imposes high cognitive demands. A central indicator in support of this view is the fact that the size of social groups is correlated with the relative volume of neocortex. (p.247)