The mutual residing refers to a relationship of the most intimate kind. The intimate relationship Jesus enjoys with the Father is a model of the one the disciples can expect with Jesus. The disciples hear Jesus when he tells them he will dwell in them and they in him. But they don't quite understand. Jesus is making a point critical to understanding his relationship with the Father.
Love leads to obedience and obedience to love.
Jesus resides with the Father. The Father will reside in the one who loves and obeys Christ. Likewise, the one who does not love Jesus does not obey his words. There is only one explicit commandment found on the lips of Jesus. That is the commandment to love one another.