c. 1200, "free from duplicity, upright, guileless; blameless, innocently harmless," also "ignorant, uneducated; unsophisticated; simple-minded, foolish," also as a surname, from Old French simple (12c.) "plain, decent; friendly, sweet; naive, foolish, stupid," hence also "wretched, miserable," from Latin simplus or simplex, "simple, plain, unmixed," literally "one-fold" (see simplex).
The sense evolution is from the notion of "without parts" or "having few parts," hence "free from complexity or complication." Compare the similar sense evolution of silly. The extended senses in Latin simplex were "without dissimulation, open, frank, guileless, direct, ingenuous," sometimes "too straightforward, too blunt," but Latin seems not to have had the "simple-minded" meaning.
The sense of "free from pride, humble, meek" is from mid-13c. As "consisting of only one substance or ingredient" (opposite of composite or compounded) it dates from late 14c.; as "easily done, presenting no difficulty or obstacles" (opposite of complicated) it dates from late 15c.; that sense also was in Latin.
From mid-14c. as "unqualified; mere; sheer," a sense also found in Latin; also "clear, straightforward; easily understood." From late 14c. as "single, individual; whole." From late 14c. of clothing, etc., "modest, plain, unadorned," and of food, "plain, not sumptuous." In medicine, of fractures, etc., "lacking complications," late 14c. As a law term, "lacking additional legal stipulations, unlimited," from mid-14c.
The Middle English word had senses that have been lost, including "inadequate, insufficient; weak, feeble; mere; few; sad, downcast; mournful; of little value; low in price; impoverished, destitute," and, of hair, "straight, not curly."