Clytemnestra was the sister of Helen, later known as Helen of Troy. Helen was the wife of the Menelaus, king of Sparta, while Clytemnestra was the wife of Menelaus' brother, Agamemnon, who was the king of Argos (Mycenae). During Agamemnon's long absence during the Trojan War, Clytemnestra had an affair with Aegisthus, her husband's cousin, and together they plotted to murder him on his return home. In some versions it is Aegisthus who does the deed, while in other versions it is Clytemnestra herself who carries out the crime. That is implied here: you can see that Clytemnestra has an axe in her hand, and it's dripping blood.
Aegisthus then ruled Argos as king, with Clytemnestra as his queen. In the end, though, Orestes, the son of Clytemnestra and Agamemnon, murdered his mother along with Aegisthus. You can read more about Orestes in this Wikipedia article.
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