Paul prays for God's gift of faith and love, and through these, for the experience of the love of Christ.
Christ lives in Christians through their faith and love so that they can 'know' 'the love of Christ' that is to 'experience' rather than merely 'comprehend' the wide-reaching and all-embracing nature of Christ's love. - "the breadth and the length, the height and the depth." Paul also praises God magnificently, indicating that the whole aim of our salvation is God's glory. God's plan of salvation, is unimaginable to us without faith and love.
When Christians are "filled with the utter fullness of God" (Eph. 3:19), they are ready to accept the experience of the fire Jesus speaks of in Luke 12:49. So he speaks of the social divisiveness that will follow, and which He illustrates with images of family dissension.
Even within each person, there will be struggles between the desire to be with Jesus, and a shrinking from the burning Cross of redemption He offers, which is also a demand for faithful following, even through conflicts and divisions.
Dear Lord, we are challenged to look not for superficial peace on earth, but for fullness of God, with lives of faith and love, achieved with much sacrifice.