From Middle English helen, from Old English hǣlan ("to heal, cure, save, greet, salute"), from Proto-West Germanic *hailijan, from Proto-Germanic *hailijaną ("to heal, make whole, save"), from Proto-Indo-European *koyl- ("safe, unharmed").
Cognate with Scots hale, hail, Saterland Frisian heila, heilen, West Frisian hielje, Dutch helen ("to heal"), German heilen ("to heal"), Danish hele, Swedish hela ("to heal"). More at whole.