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mid-14c., "freeing from temporal punishment for sin," from Old French indulgence or directly from Latin indulgentia "complaisance, fondness, remission," from indulgentem (nominative indulgens) "indulgent, kind, tender, fond," present participle of indulgere "be kind, yield," of unknown origin; perhaps from in- "in" + derivative of PIE root *dlegh- "to engage oneself."
Sense of "gratification of another's desire or humor" is attested from late 14c. That of "yielding to one's inclinations" (technically self-indulgence) is from 1640s. In British history, Indulgence also refers to grants of certain liberties to Nonconformists under Charles II and James II, as special favors rather than legal rights; specifically the Declarations of Indulgence of 1672, 1687, and 1688 in England and 1669, 1672, and 1687 in Scotland.
Note: In the Middle Ages, indulgences were frequently sold, and the teaching on indulgences was often distorted. The attack by Martin Luther on the sale of indulgences began the Reformation.