We, humans, have evolved pretty big brains compared to other mammals, and even compared to our primate cousins. Recent research seems to have found the reason for the higher number of neurons in our brains (about 86 BILLION). It appears that a single gene is responsible for our bigger brain.
The Neanderthals are extinct human species which despite having similar sized brains, had a different brain structure and composition to ours. To try and explain these differences, researchers examined the genomes of Neanderthals and modern humans (H. sapiens) and compared them in search for genetic differences, particularly in the cells giving rise to neurons in the neocortex. The neocortex, as it name indicates, comprises the more “modern” parts of our brain located behind the forehead and home to the more complex cognitive functions.
If you want to know the identity of this special gene, check MappingIgnorance.org