"move by turning and twisting," Middle English winden, from Old English windan "to turn, twist, plait, curl, brandish, swing" (class III strong verb; past tense wand, past participle wunden), from Proto-Germanic *windan "to wind," from PIE *wendh- "to turn, wind, weave" (source also of Latin viere "twist, plait, weave," vincire "bind;" Lithuanian vyti "twist, wind").
The verb wend is its causative form, and it is not always clear in Middle English which is meant. Also compare wander. The past tense and past participle merged in Middle English.
The meaning "to twine, entwine oneself around" is from 1590s; the transitive sense of "turn or twist round and round (on something) is from c. 1300. The meaning "set a watch, clockwork, etc. in operating mode by tightening its spring" is from c. 1600.
To wind down "come to a conclusion" is recorded from 1952; to wind up "come to a conclusion" is recorded from 1825; it was used earlier in a transitive sense of "put (affairs) in order in advance of a final settlement" (1780).
Of a corpse, "to enshroud" (c. 1300), hence winding sheet (n.), attested from early 15c.
Germanic cognates include Old Saxon windan, Old Norse vinda, Old Frisian winda, Dutch winden, Old High German wintan, German winden, Gothic windan "to wind."