c. 1300, "care, heed," from Latin cura "care, concern, trouble," with many figurative extensions over time such as "study; administration; office of a parish priest; a mistress," and also "means of healing, successful remedial treatment of a disease" (late 14c.), from Old Latin coira-, a noun of unknown origin. Meaning "medical care" is late 14c.
late 14c., "to restore to health or a sound state," from Old French curer and directly from Latin curare "take care of," hence, in medical language, "treat medically, cure" (see cure (n.1)). In reference to fish, pork, etc., "prepare for preservation by drying, salting, etc.," attested by 1743. Related: Cured; curing.
Most words for "cure, heal" in European languages originally applied to the person being treated but now can be used with reference to the disease. Relatively few show an ancient connection to words for "physician;" typically they are connected instead to words for "make whole" or "tend to" or even "conjurer." French guérir (with Italian guarir, Old Spanish guarir) is from a Germanic verb stem also found in in Gothic warjan, Old English wearian "ward off, prevent, defend" (see warrant (n.)).