Her short brown hair was curled in a puffy bouffant hairdo.
Big hair refers to a bouffant hairstyle, especially one in which long hair has been sprayed, permed, or teased to make it stand away from the head and give it volume.
"I lived with a bouffant atop my brain from 1977 to 1979, back when it hadn't been in style for ten years," my mother told me.