This is the 149th most frequent Korean word.
미국의
"American"
In this sentence, "미국의" functions as a possessive, meaning 'of the United States.' It describes '수도' (capital) as belonging to the United States.
미국의 수도는 워싱턴 D.C.입니다.
The capital of the United States is Washington, D.C.
Here, "미국의" is used to denote that the subject '문화' (culture) is associated with the United States.
미국의 문화는 매우 다양합니다.
The culture of the United States is very diverse.
In this context, "미국의" specifies that the '역사' (history) being studied pertains to the United States.