Adam Kircher and Karen K. Glendenning in their The Evolution of Human Intelligence and Neural Inhibition say that the main biological correlate of the intelligence of humans is with the increase in size of the neocortex (cerebrum or just plain cortex).
In addition to the size of neocortex, they propose the amount of neural inhibition to which the cortex is subjected may play a major role in human intelligence.
The cerebrum or cortex is the largest part of the human brain, associated with higher brain function such as thought and action.
Across nearly seven million years, the human brain has tripled in size, with most of this growth occurring in the past two million years.
John Hawks, a professor of anthropology at the University of Wisconsin–Madison, explains:
For the first two thirds of our history, the size of our ancestors' brains was within the range of those of other apes living today. The species of the famous Lucy fossil, Australopithecus afarensis, had skulls with internal volumes of between 400 and 550 milliliters, whereas chimpanzee skulls hold around 400 ml and gorillas between 500 and 700 ml.
During this time, Australopithecine brains started to show subtle changes in structure and shape as compared with apes. For instance, the neocortex had begun to expand, reorganizing its functions away from visual processing toward other regions of the brain. - ScientificAmerican.com
The cerebral cortex is highly wrinkled. Essentially this makes the brain more efficient, because it can increase the surface area of the brain and the amount of neurons within it.
Discover some of the fascinating facts and figures about the human brain, shared by BeBrainFit.com and learn 11 ways to increase IQ, featured at MentalHealthDaily.com.