The vase painting shows Briseis, who had been given to Achilles as a war prize. When Agamemnon was compelled to give up his own prize, he demanded Briseis in compensation. The vase shows her being taken away from Achilles to be given to Agamemnon... whence the wrath of Achilles. The story is famously told in Book I of Homer's Iliad.
You can also find more myths and legends for the week of November 4-10 here. For more information and links to the actual javascript code, see the Myths & Legends Widget Reference Page.