The wrinkles on the surface of the brain (this part is called the cortex) are actually folds in the tissue. The upward ridges like hills are called ‘gyri’ and the downward gaps like valleys are called ‘sulci’. The reason these folds are so important is that they allow us to compact a large amount of cortex into a small space by folding it like a concertina. You can watch a video of mathematically unfolding the cortex here: http://www.cogsci.ucsd.edu/~sereno/unfoldorig.mpg (it is probably best to use the slider to watch it in slow motion as the video is quite fast).
It is not just the folds but the different layers of cells that make up this folded brain tissue that are important (humans have 6 layers of cells in the cortex). The minke whale having one of the largest brains in the world has far less neurons packed into the cortex (5 cortical layers of cells). One study that tried to calculate the difference in the number of neurons in the cortex of a minke whale and a human, found that humans had about 3 times as many neurons in the cortex as the whale, despite the whales much larger brain over all.
It is thought that having so many tightly packed neurons that can form connections with one another is what gives us such good thinking abilities.