Japanese for "inside looking" or more succinctly "introspection'.
It's a type of therapy, if you will, where one examines one's relationships with others, and reflects on them. This reflection is not a free for all, but structured around three questions:
What have I received?
What have I given?
What troubles or difficulties have I caused?
These questions are typically applied towards the people in one's life, sitting, reflecting, and writing down the answers. The answers remind one that the people in one's life provide a lot, perhaps more than is required by what one gives. The last question also brings home how much trouble one has caused these people. This is a blindspot in most people's perception of how they relate to others.
In answering these questions, one develops a sense of gratitude towards others, and uses this to become a better person.
Reference - http://www.anamorph.com/todo/naikan.html