International health means two different, but related, things. It means care of people who travel from one country to another, and knowledge of diseases foreign to the traveler. It also means people from one country trying to improve health in another.
There are different kinds of groups that are involved in international health. They engage in international health for different reasons and with different ethics and rules.
Governments of rich, "developed" countries are often interested in the health of other countries. They are especially interested in the health of neighbor countries. The reasons for this are many: if they have extra resources, they may want to share them with their neighbors; but also they may want to stop spread of diseases from their neighbor country across the border. For example, the United States is a richer country than Mexico and has little problem with measles (in children) or rabies (in mammals) in the interior, but along the border with Mexico these diseases are more common.
The Western Hemisphere's countries have formed PAHO, the Pan American Health Organization, to deal with these kinds of problems in an organized way. PAHO knows that people and goods flow across borders in both directions, and a problem in one country will soon be a problem in its partner countries. PAHO is an example of an international organization.
Non-governmental organizations (NGOs) are associations organized outside of the government by volunteers and others, and which serve a particular interest. Often, NGOs interested in health perform important functions in international health, both in direct care and in development.