In ancient Greece the Mystai were the initiates of the Eleusinian Mysteries of the Goddess, Demeter.
There were two Eleusinian Mysteries, the Greater and the Lesser. According to Thomas Taylor, "the dramatic shows of the Lesser Mysteries occultly signified the miseries of the soul while in subjection to the body, so those of the Greater obscurely intimated, by mystic and splendid visions, the felicity of the soul both here and hereafter, when purified from the defilements of a material nature and constantly elevated to the realities of intellectual [spiritual] vision." According to Plato, "the ultimate design of the Mysteries was to lead us back to the principles from which we descended, a perfect enjoyment of intellectual [spiritual] good."
The Lesser Mysteries took place in the month of Anthesteria under the direction of Athens' archon basileus. In order to qualify for initiation, participants would sacrifice a piglet to Demeter and Persephone, and then ritually purify themselves in the river Illisos. Upon completion of the Lesser Mysteries, participants were deemed mystai ("initiates") worthy of witnessing the Greater Mysteries.
From Wikipedia: https://en.wikipedia.org/wiki/Eleusinian_Mysteries
There is also a modern Tradition of Dianic Witchcraft who refer to themselves as Mystai and who work with the Goddess, Hekate. http://mystaiofthemoon.com/about.htm