"strong thread made from twisted strands," Old English twin "double thread," from Proto-Germanic *twiznaz "double thread, twisted thread" (cognates: Dutch twijn, Low German twern, German zwirn "twine, thread"), from the same root as twin (adj.).
"to twist strands together to form twine," c. 1300, from twine (n.) and probably also from Old Norse tvinna "to double." Sense of "to twist around something" (as twine does) is recorded from late 14c. Related: Twined; twining.