Sciron was a famous robber, a son of Poseidon or Pelops. He had developed the idiosyncratic practice of forcing passing travellers to wash his feet as he stood on a cliff-top by the sea on the border between Attica and Megaris on the isthmus of Corinth.
As they did so, he gave them a hefty kick and sent them into the sea, where a giant turtle devoured their bodies. (Theseus eventually put an end to this by paying him back in his own coin - he booted him off the cliff into the sea.) We have a choice here: sciron means 'parasol', sciros means 'gypsum'.
The former may refer to a type of sacrifice in which a victim was pushed from a cliff-top into the sea carrying a token parachute; the latter could mean 'limestone' and refer to the rock of the cliff. Parasols were by no means unfamiliar objects to the Greeks: at an annual women's festival in Athens, priestesses processed carrying parasols. (This ceremony was called the Scirophoria, 'parasol-bearing', and gave its name to one of the Greek months, Scirophorion, which corresponded to the latter half of June and the first half of July.)