The encyclical letter Laudato Si is available here on the Vatican website. Conversion is change. But in the Christian context, it means an examination of conscience, and an admission of sin and guilt.
218. In calling to mind the figure of Saint Francis of Assisi, we come to realize that a healthy relationship with creation is one dimension of overall personal conversion, which entails the recognition of our errors, sins, faults and failures, and leads to heartfelt repentance and desire to change. The Australian bishops spoke of the importance of such conversion for achieving reconciliation with creation: “To achieve such reconciliation, we must examine our lives and acknowledge the ways in which we have harmed God’s creation through our actions and our failure to act. We need to experience a conversion, or change of heart”.[Australian Catholic bishops’ Conference, A New Earth – The Environmental Challenge (2002)]