The ring around the iris is called the limbal ring. It is a dark ring that varies depending on the color of the iris, and enhances the brightness of the sclera.
Prominent limbal rings were found to be regarded as more attractive than thin limbal rings in both males and females in a 2011 University of California at Irvine study. The limbal ring is most vibrant during the early 20s, then often fades or disappears as people age. The limbal ring is formed where the sclera and the iris meet, and its prominence is often regarded as a sign of youth.