Unclear, ambiguous, or confusing.
Example:
All she could get from the old woman were a few delphic comments that left her more confused than ever about the missing documents.
Delphi in Greece was the site of a temple to Apollo at which there was an oracle, a woman through whom Apollo would speak, foretelling the future. The Greeks consulted the oracle frequently on matters both private and public. The prophecies were given in obscure poetry that had to be interpreted by priests, and even then was subject to disastrous misinterpretation. Modern-day descendants of the oracle include some political commentators, who continue to utter words of delphic complexity each week.