Paul is saying that what the Spirit does in us is to draw us into a relationship, a loving relationship into which we are adopted as children of God. This relationship is the relationship between Jesus and his Abba or Father. As the Spirit brings Christ's life to birth in our life, we find ourselves sharing with Christ in the most central and characteristic aspect of his life - namely the relationship that defines him and marks him as God's beloved child, his relationship with God as the loving source of his whole life. And more wonderfully yet, we find that we do not remain mute observers of this relationship but that the Spirit actually teaches us the very language of Jesus' conversation with the Father. The Spirit puts Jesus' words of loving adoration and trust in our own hearts and makes it possible for us to speak them ourselves.
(Mysteries of Faith, p.15)