1550s, "mildness or gentleness shown in exercise of authority," from Latin clementia "calmness, gentleness," from clemens "calm, mild," related to clinare "to lean" (see lean (v.)) + participial suffix -menos (also in alumnus). For sense evolution, compare inclined in secondary meaning "disposed favorably." Earlier in same sense was clemence (late 15c.).
Meaning "mildness of weather or climate" is 1660s (a sense also in Latin); clement (adj.) is older in both senses, late 15c. and 1620s respectively, but now is used only in negation and only of the weather.