Darwin introduced Natural Selection in 1859 book, "On the Origin of Species". In this book there was a very small reference to Sexual Selection, which was to later become an overriding concern driving his future work. His next book, "The Descent of Man, and Selection in Relation to Sex", 1871, addressed sexual selection more directly.
According to Natural Selection, species change to adapt to the environment and the traits that are the fittest for the environment survive and are passed on in time. Thus, Natural Selection cannot explain traits like (Darwins favourite) peacock feathers having survived, or indeed evolved. What is the survivalistic advantage of a brightly coloured plume that draws the attraction of all your natural predators when in action?
Sexual Selection fills this gap by saying that the females of the species select the males they will mate with. Due to the differential parental investment quotient, females are far fussier. Thus, the male of the species will often evolve a trait whose whole purpose is to impress the female, and which has no direct environmental survivalistic rationale. Like the peacock feather. It impresses the female with the quality of this male's genes and good health, because it is something he cannot fake.
The neo cortex was developed relatively recently in evolution. Before that the old brain handled almost all our survival needs. The neo cortex is responsible for consciousness, poetry, art, executive control, social behaviour, languages.
These are not skills a primate that has just come down from the trees needs to survive. Besides, nature always devises the most economical solutions to the most pressing survival challenges thrown by a changing environment. So why develop such a massive huge brain, the bulk of which is the neocortex, and the bulk of which most people dont use or need?
In humans the neo cortex contributes to the bulk of the huge brain size difference with its predecessors. The "swollen head" solution has huge implications on how the primate will now develop, and thereby how the adult will live to enable that development. The head has grown bigger than the pelvis can accomodate, so the infant is now born with only a small fraction of the brain development he is going to have as an adult. Most of the brain growing happens in the early years of a child. As a consequence, while any other animal is reasonably self sufficient from birth, horses can just get up and run with the herd, the human baby has to be nurtured for years while this massive and largely unnecessary brain grows and is programmed, by the parents. Thus it needs the mother to stay by its side through this period, dedicated to training and protecting it. It needs a completely different (male in resifence) family/social structure to protect this mother child set up while the mother is preoccupied with the baby, it needs the male to be able to go get food and come back and share it with his mate, over a prolonged period of time, thus requiring emotions and love to develop, it needs a herd in residence to protect the females and children while the males are out hunting (we started eating meat around now, so the men have to go hunt afar) and thuse giving rise to society, moral, group feelings.
It changes everything ...
Why do we have this neo cortex? What do we do with it? We write poems and make pictures and invent things, which impresses the women of our genetic quality and resourfulness (yes and we amass resources - get rich).
The famous Phineas Gage, on whom the book "An Odd Kind of Fame", by Malcolm Macmillan, was based, survived for 15 years after losing a huge part of hs cortex, when a meter long tamping iron with a diameter of 1.25 inches (3.2 cm) weighing thirteen and about six kilos entered his skull below his left cheek bone and exited after passing through the anterior frontal cortex and white matter. He suffered "some" changes in emotional and social processing, but he was alive. for fifteen years.
Infact, Egas Moniz, received the Nobel Prize for starting the frontal lobotomy, in which this part of the brain is removed or destroyed. Later, Walter Freeman imported the operation to america and popularised it there.
Moniz develops lobotomy for mental illness
Relatives of Lobotomy Patients Want Nobel Prize Revoked
Article on sexual selection by Paul R Ehrlich, David S Dobkin and Darryl Wheye
Co-evolution of neocortex size, group size and language in humans by RIM Dunbar
Neocortex size and social network size in primates, paper by H Kudo and RIM Dunbar
The Piraha People at Wikipedia
The Blue Brain project.