To stop someone from being angry or discontented; to placate or pacify. The manager tried to conciliate the upset customers by offering them a discount.
To act as a mediator or go-between in a dispute in order to bring about an agreement or reconciliation. The diplomat was sent to conciliate between the two warring nations.
To win or gain the favor, goodwill, or support of someone by friendly or accommodating acts. The candidate tried to conciliate undecided voters with promises of tax reform.