What is the advantange of the cerebrum of the brain being wrinkled?

The "wrinkles" of the brain increase the surface area of the brain.

The involutions are called sulci or fissures, and the bumps in-between these involutions are called gyri.

Most of your brain cells are within the gray matter of the brain & most of your gray matter is in the outer layer of the brain. Therefore, if you increase the surface area of your outer layer of the brain with sulci and gyri, it creates more cortex for our limited sized skulls. The cortex is the main wrinkled part of our brain, and is responsible for much of our conscious experience.

In "lower" mammals such as mice, the brain is smooth.

Stretched out an average human brain is about 2.5 square feet in size.