The peacock was Hera's sacred animal.
Once, Zeus, the king of the gods, fell in love with Io, a priestess of Hera. Jealously, his wife Hera asked from Zeus to bring her the young girl- and when he brought her, Hera immediately transformed Io into a cow.
Afterwards, Hera gave the transformed girl to her servant Argos, an all-seing monster that had hundred eyes all over his body. His mission would be to guard Io.
Zeus felt sorry for Io and tried to help her. Therefore, he called his messenger Hermes and gave him the order to kill Argos. Hermes approached the monster and started playing the flute to hypnotize him. Soon the monster fell into a deep sleep and Hermes took a stone and destroyed him.
However, Hera knew all about the plan and had already removed the eyes of Argos the day before. So after Argos' death, Hera transferred all his eyes to the tail of a peacock to thank and honor her servant.