What specifically would the experience of living and working in another country contribute to your skills and effectiveness as a manager in the United States America?
Many of the specifics in answer to your question would depend upon where you worked overseas and what type of management position you assumed in the United States.
In many parts of the world, living and working in another country would involve becoming fluent in another language and adjusting to the lifestyle of a different culture. These experiences could help you develop empathy toward the viewpoints and needs of others, and would assist you in understanding the need to cooperate and communicate with people who have different backgrounds and ideas than you do-important qualities for a successful manager.
Being exposed to how business functions and in perceived in another country may give you insights that could be helpful in developing marketing strategies or new products to be offered in foreign countries by the American firm that employs you. You may be able to provide important insight into trade regulations, availability of resources, or possible venues to display your company's product.