Where does it come from
As mentioned above, the Delphi method owes its name to the Delphos oracle, where one or more pythonesses provided advice and answers to those who came to the sanctuary with a query or problem. The work of the pythonesses consisted of invoking the god Apollo and transmitting their information to a priest who then interpreted it and delivered it to the querent.
According to Wikipedia, the origins of the Delphi technique in contemporary society date back to the Cold War when it began to be used to predict the impact of technology on conflict. In this context, in 1944, General Henry H. Arnold ordered a report to be drawn up on the technologies that might be developed by the military in the future. Various approaches were tried, but it soon became apparent that traditional methods of technology prediction were deficient in areas where scientific laws had not yet been determined. To overcome these shortcomings, the RAND Project started (Olaf Helmer, Norman Dalkey and Nicholas Rescher), whereby several experts gave their opinion on the probability, frequency and intensity of possible enemy attacks. Other experts provided corresponding feedback. This process was repeated several times until a consensus was reached.
While the Delphi Technique originated and was first used in business, it has since been used in a variety of other settings, including educational settings. Since the early 1970s, the Delphi technique has been used in health science to sort out priorities in health care research and to develop education, qualifications, and the work of health care staff. The technique is thought to produce accurate forecasts of future trends.