Why was Kennedy interested in doing things like creating the Peace Corps to help developing nations?
There were two major reasons why President Kennedy wanted to create a Peace Corps (though we must be clear that he was not the one who came up with the idea). One was altruistic and the other was more connected to American national interests.
On the altruistic side, Kennedy wanted to help poorer countries. The Peace Corps was meant to provide technical support for projects that would help with development in poorer countries. By creating this group, Kennedy simply hoped to help improve the lives of people around the world.
On the less altruistic side, Kennedy was interested in tying other countries more closely to the United States. By sending these volunteers out, Kennedy hoped to make the countries have more positive feelings about the United States and Americans. This would help the US in the Cold War. As more poor countries felt a connection to the US, they would gravitate to the American side of the Cold War.
Thus, Kennedy wanted to create a Peace Corps both for altruistic reasons and reasons of geopolitics.