I would define "The Way" as tradition. In many societies, people's lives are governed as much by traditions and by engrained ways of doing things as they are by actual written laws. This is the case in Kira's society. They are governed by "The Way," which a harsh set of unwritten laws that reflect the way things have "always been."
You can perhaps relate this to modern US society by thinking about attitudes towards social welfare issues here in the US. Through this book, Lowry is commenting on our own attitudes in this regard. She is pointing out how our societal prejudices and traditions work to hurt the poor and the disabled. She is pointing out that we have this traditional way of looking at the poor. We tend to think that their problems are their own fault and so we punish them for being poor. This is not really caused by laws. Instead, it is caused by our traditional attitudes.
"The Way," then, is simply the set of traditional attitudes that governs the way Kira's society runs. Lowry is trying to show us that our society is heavily influenced by our traditional attitudes and prejudices as well.