A common question posed is, "how did the eye evolve?", because the eye is so complex. However, this has been answered rather clearly and there are several examples around the world of animals in which the eye has evolved independently.
The human brain, however, only seems to have evolved once in the history of life on Earth - a brain which is capable of advanced speech, predicting the future given information on the past, producing art, imagining advanced abstract concepts such as algebra, creating advanced tools, etc.
How, then, could the human brain have evolved? What stimulus was there for progressive Homo individuals to have brains that were slightly more advanced than the previous one's? I've heard Richard Dawkins summarize it as "big brains are sexy", but that's a comment made in hindsight (and not even shared by all members of the human species today!) At the time, why would a human female choose a male with a slightly larger brain, so slightly larger that the increased intelligence probably wouldn't be noticeable? Or why would such an individual have an evolutionary advantage?