The social brain hypothesis posits that the large brain size (when compared to body size) of both human and nonhuman primates is related to their complex sociality (Dunbar, 1998). Both human and nonhuman primates exist in vastly intricate social environments that require high-functioning cognitions, such as facial recognition and identification, learning, and cooperation, to navigate successfully. The link between social complexity and brain size has been studied in a multitude of ways in both species, including group size, deception, formation of coalitions, and mating strategies. All of these aspects of sociality (and more) have been found to be positively correlated with neocortex size, and in humans, evidence suggests that there is a connection between social network size, cognitive skills, and brain volume (Dunbar, 2012). Despite the compelling support for the social brain hypothesis, much debate still exists as to the cause-and-effect aspects of brain size and social complexity.
Dunbar, R. I. (1998). The social brain hypothesis. brain, 9(10), 178-190.
Dunbar, R. I. (2012). The social brain meets neuroimaging. Trends in cognitive sciences, 16(2), 101-102.