In this line, Shakespeare is referencing a condition that, in modern times, we refer to as hyperchromic anemia. This condition, which was called the Green Sickness in Shakespeare's day, results in the skin appearing pale and green because the person lacks enough red blood cells to give skin its healthy color. In Shakespeare's time, it was often associated with virginity because physicians at the time believed the disease to uniquely affect young, unmarried women. Diana was the goddess of chastity, which is why Shakespeare describes "vestal," or virginal, livery as "sick and green."