When combined, these characters literally mean “to extinguish the incident (and) pacify the people.” This paints a clear picture: an active intervention is made to stop a conflict (the “事”) in order to bring calm back to the people (“人”) involved.
息事宁人 is a direct reflection of the central cultural value of 和 (hé) - harmony. In many East Asian cultures, and particularly in China, maintaining group harmony is often considered a higher virtue than individual expression or confrontation. Openly disagreeing, especially with a superior or elder, can cause everyone to lose “face” (面子, miànzi) and disrupt the social fabric. This contrasts sharply with many Western, particularly American, cultural ideals. In the West, “clearing the air,” “tackling a problem head-on,” and “speaking your mind” are often seen as signs of honesty and strength. Avoiding a conflict can be perceived as weakness, dishonesty, or passive-aggression. 息事宁人 is the cultural tool used to uphold harmony. It's the decision to value the relationship and the peace of the group over the need to be right. A Chinese manager might use this approach to handle a dispute between two employees, not by investigating who was “right,” but by finding a way to make them work together peacefully again. This is not necessarily about justice, but about social and operational stability.
This idiom is frequently used in various contexts, and its connotation can shift from positive to negative depending on the situation.