The Mounikia arose from the following tale: a bear that dwelt about Artemis' temple in Athens was killed. Artemis was displeased and sent plagues among the people. They consulted the Oracle at Delphi to learn what they had to do to placate Her, and they were told that someone must sacrifice their daughter. Her father dressed a goat up to look like her, and offered it instead. Artemis accepted the offering, and the town celebrated the removal of the plagues with dancing and cakes "shining all around" that were meant to look like full moons. This lunar aspect of the festival relates to Artemis shining Her protection on the city of Salamis.
Mounikia 2015
Reference
Minai, T. (2007). Dancing In Moonlight: Understanding Artemis Through Celebration. Hubbardston, MA: Asphodel Press.