evolution - How did the human brain evolve?

why would such an individual have an evolutionary advantage?

First thing to keep in mind, is that natural selection will seize upon even very slight advantages and evolve them until the point where evolving them is no longer viable. So, to you a slight increase in intelligence might be unnoticeable, but in a naturally selecting system it would be very noticeable. Don't mix up sexual selection (where the preference of one sex shapes the selection of genes) with natural selection (where fitness to the environment shapes the selection of genes). Sexual selection may or may not have helped shape brain evolution, I can't produce evidence that it did.

But the increased fitness that slight gains in intelligence convey are easier to create evolutionary anecdotes about. It's simplistic to speak of just "intelligence" as evolving. Many different nervous structures evolved through out the animal kingdom, each with a function that directly increased fitness. I get the feeling that you're specifically talking about the evolution of the neocortex, because you reference human intelligence.

So, what I guess you're really asking is what evolutionary advantage does the neocortex convey? The answer isn't that hard, once you understand a little about the neocortex. It is an organ that simply models the external and internal world as perceived by your sensory organs. By external world, I mean modeling things like vision, hearing, touch, etc... By internal world, I mean modeling the actions you can perform, the plans you make, and so on. Increasing the size of the neocortex is essentially increasing the possible complexity of these models. Not only can you find more subtle and complex patterns out there, you can develop increasingly subtle plans and ruses too.

Watching documentary footage of tribal hunters provides a really stark look at just how useful the neocortex is. It frames our intelligence in terms of a situation similar to one we evolved in. It's not hard to imagine why the growth has been explosive. Outsmarting other animals is a great niche that in our evolutionary history was virtually unexploited.