I love this name so I did a bit of research on it awhile back.
The name of the island is pre-Celtic, meaning unknown. These are two traditional interpretations, although neither is etymologically correct:
1) "Winged (island)", from Gaelic "sgiath": the island's great peninsulas thrust out north and south like wings. 2) From Gaelic "sgian", meaning "knife", with reference to the deep cuts in Skye's coastline.
To reiterate, neither of the above is the real etymological meaning, but they are often quoted as that. It's like Katherine, which is constantly quoted as meaning "pure", because people associated it with this, even though the real derivation is lost.