Why is the US concerned about some of the countries around the world? (please give examples)

America's interest in a country usually involves economic or military considerations.

In Iraq, for example, the United States has a strategic military interest. Iraq shares a long border with Iran, a country that has shown significant hostility toward the United States (we've all seen the burning flags and heard the “death to America” chants). As an example of how fluid international relations can be, Iraq's importance has changed since our invasion in 2003. The development...

America's interest in a country usually involves economic or military considerations.

In Iraq, for example, the United States has a strategic military interest. Iraq shares a long border with Iran, a country that has shown significant hostility toward the United States (we've all seen the burning flags and heard the “death to America” chants). As an example of how fluid international relations can be, Iraq's importance has changed since our invasion in 2003. The development and rise of ISIS in Syria and Iraq has made Iraq more important than ever. As long as ISIS can operate as a quasi-state in the Middle East, it can continue to recruit and perpetrate terrorist attacks. A strong Iraq would have made ISIS's territorial gains impossible. So the U.S. continues to support Iraq militarily, and at least one of the reasons is ISIS.

The U.S. also has many economic interests throughout the world. Economies improve with trade with other countries. Robust trade boosts a country's export business while making it possible to import products for which there is a market. To this end, establishing trading partnerships with growing economies can benefit the U.S. economy. Brazil is a good example of an important U.S. trading partner. Most people would probably be surprised to find out that Brazil is the world's seventh largest economy. That's a lot of economic clout. The office of the United States Trade Representative reported the following export statistics:

U.S. goods exports to Brazil in 2015 were $32 billion, down 25% ($11 billion) from 2014 but up 106% from 2005. U.S. exports to Brazil account for 2.1% of overall U.S. exports in 2015.

A lot of U.S. jobs are made possible by this much trade.

The office also reported the following import statistics:

The top import categories (2-digit HS) in 2015 were: mineral fuels ($4.5 billion), aircraft ($3.0 billion), iron and steel ($2.9 billion), special other (articles for repair and returns) ($2.6 billion), and machinery ($1.7 billion).

When this much money and product is changing hands, the economic impact on both countries is significant. For it's own economic well-being, the U.S. has to pay attention to what is going in countries like Brazil.