The wrinkles in the brain increase the brain's surface area. By increasing the surface area of the brain, humans can increase the size of their brains and improve their ability to function at high levels. Humans have evolved to have wrinkles in their brains to be distinguished from animals.
The wrinkles in the human brain are known as sulci and gyri. How Stuff Works explains that the ridges in the brain are called gyri, and the crevices are called sulci. Many of these ridges and crevices also have specific names, which allow neuroscientists to differentiate these parts of the brain. Fetal brains are relatively smooth, but as the fetuses become full-term babies their brains start to develop sulci and gyri.