From late 14c. as "act or process of explaining or interpreting; an explanation; construction placed upon an action." Meaning "dramatic or musical representation" is from 1880.
"exposition or interpretation of the Hebrew Scriptures," 1610s, from Hebrew (Semitic) midhrash, from darash "tread, frequent, seek, search, apply oneself to."
late 14c., "interpretation of signs, dreams, and omens," also "a supposing, a surmising," from Old French conjecture "surmise, guess," or directly from Latin coniectura "conclusion, interpretation, guess, inference," literally "a casting together (of facts, etc.)," from coniectus, past participle of conicere "to throw together," from assimilated form of com "together" (see con-) + iacere "to throw" (from PIE root *ye- "to throw, impel").
Sense of "an unverified supposition" is from 1520s; that of "act of forming of opinion without proof" is from 1530s.