To soften, in a figurative sense; to allay, mitigate, ease, or lessen, as heat, pain, or grief; to appease or pacify, as passion or tumult; to satisfy, as appetite or desire.

satisfy (thirst); "The cold water quenched his thirst"

provide physical relief, as from pain; "This pill will relieve your headaches"

To abate or subside.

cause to be more favorably inclined; gain the good will of; "She managed to mollify the angry customer"