Perseus, son of the king of Athens, is sent by the Goddess Athene to a quest for the head of the gorgon Medusa. Medusa is a snake-haired monster living in Asia minor. Her ability is to petrify any attacker. Perseus wins severeal special weapons from the Gods at secondary quests, a magic hood of Hermes is one of it. Finally he finds and decapitates Medusa. On his way back, he frees Andromeda, daughter of a local king who should be sacrificed to a sea monster. Of course the hero marries the princess. Her previous fiancé, looking for vengeance, was killed by Perseus by pertrifying him using Medusa's head. Andromeda and Perseus travel back to Athens.

So far the antique writers. To modern research, matters look a little bit different. Today it is a known fact during the bronze age patriarchal dominated tribes entered the mediterrean area, displacing the old matriarchal societies [2]. During this process, some of the Goddesses of the old societies were integrated into the pantheon of the intruders (as "wifes") others became monsters which must be slayed down.
There are hints the Earth Goddess was worshipped in Asia minor in the shape of a winged snake. Her priestesses wore snake-decorated masks in ceremonies [1]. The "decapitation" from the saga originally could have been well a pulling down of the mask of a priestess (think about the symbolism of it!). Medusa's snake hair would have been nothing else but the decoration of the mask, and Perseus a boy who fully failed his own initiation rite. (I agree in the opinion he was punished to get a helpless spoiled princess instead of a wise selfconscious priestess [5].)
Also to this points the fact he was sent to his quest by Athena. Connections of Athena and Medusa show originally they were aspects of one Goddess of wisdom [1]. The "mind dominated" part of Her was integrated as Athene to the intruders' pantheon, while the mysterious-dark part became "Medusa the monster". Such splittings have become known from other deities as well, for example Python-Apollon [3].

Interestingly, there also is some completely different meaning of the word "Medusa". In Egyptean, "medu" (transcription mdw) means "to speak" as well as "the word". Appending an "s" the transcription changes to "mdw.s" which can be read "Medusa". Grammatically, it means "she speaks" or "by her word" [6].
Thus, "Medusa Iseum" has the hidden meaning "Iseum, which is (exists) by Her word". Sometimes the ways of the Goddess are of a quite selected cleverness...

[1] Le Van, Alicia: The Gorgon Medusa. Final Paper/Women in Antiquity course, http://www.perseus.tufts.edu/classes/finALp.html
[2] Zingsem, Vera: Göttinnen großer Kulturen. DTV, Munich 1999.
[3] Cerny, Christine: Das Buch der Naturgeister. Goldmann Verlag, Munich 1997.
[4] Apollodor: Bibliotheke, II 39-48.
[5] Rt. Rev. C.Wehmeyer (F.O.I.), personal communication.
[6] Graefe, Erhart: Mittelägyptisch - Grammatik für Anfänger. 5. Aufl., Harrassowitz Verlag, Wiesbaden 1997.