1570s, from Modern Latin sceleton "bones, bony framework of the body," from Greek skeleton soma "dried-up body, mummy, skeleton," from neuter of skeletos "dried-up" (also, as a noun, "dried body, mummy"), from skellein "dry up, make dry, parch," from PIE root *skele- "to parch, wither" (see sclero-).
Skelton was an early variant form. The noun use of Greek skeletos passed into Late Latin (sceletus), hence French squelette and rare English skelet (1560s), Spanish esqueleto, Italian scheletro. The meaning "bare outline" is first recorded c. 1600; hence skeleton crew (1778), skeleton key, etc. Phrase skeleton in the closet "source of secret shame to a person or family" is from 1812 (the image is perhaps from the Bluebeard fable).