The sense of "to give up desire or power to punish" (late Old English) is from use of such a compound as a Germanic loan-translation of Vulgar Latin *perdonare (Old Saxon fargeban, Dutch vergeven, German vergeben "to forgive," Gothic fragiban "to grant;" and see pardon (n.)). Related: Forgave; forgiven; forgiving.
c. 1300, pardoun, "papal indulgence, forgiveness of sins or wrongdoing," from Old French pardon, from pardoner "to grant; forgive" (11c., Modern French pardonner), "to grant, forgive," and directly from Medieval Latin perdonum, from Vulgar Latin *perdonare "to give wholeheartedly, to remit," from Latin per "through, thoroughly" (from PIE root *per- (1) "forward," hence "through") + donare "give as a gift," from donum "gift," from PIE *donum "gift," from root *do- "to give."
Meaning "a passing over of an offense without punishment" is from c. 1300, also in the strictly ecclesiastical sense; the sense of "pardon for a civil or criminal offense; release from penalty or obligation" is from late 14c., earlier in Anglo-French. Weaker sense of "excuse for a minor fault" is attested from 1540s. To beg (one's) pardon "ask forgiveness" is by 1640s.
Strictly, pardon expresses the act of an official or a superior, remitting all or the remainder of the punishment that belongs to an offense: as, the queen or the governor pardons a convict before the expiration of his sentence. Forgive refers especially to the feelings; it means that one not only resolves to overlook the offense and reestablishes amicable relations with the offender, but gives up all ill feeling against him. [Century Dictionary]
c. 1500, "pleasing, agreeable" (a sense now obsolete), from Old French placable "forgiving, conciliatory" and directly from Latin placabilis "easily appeased or pacified," from placare "to calm, appease, quiet, soothe, assuage," causative of placere "to please" (see please). From 1580s as "capable of being pleased or pacified, easily appeased, willing to forgive." Related: Placably; placability.