"undivided devotion"
Having multiple commitments necessarily leads to division and conflicts of interest. This is especially problematic in our relationship to God. Paul warns of this in his advice about marriage:The unmarried man is anxious about the affairs of the Lord, how to please the Lord; but the married man is anxious about worldly affairs, how to please his wife, and his interests are divided.
Paul's concern, though, is not just about marriage. A few verses earlier, he recommends that "those who buy [be] as though they had no goods, and those who deal with the world [be] as though they had no dealings with it." Paul is warning about divided loyalties, warning us to avoid conflicting commitments, "to secure your undivided devotion to the Lord."
And the unmarried woman or girl is anxious about the affairs of the Lord, how to be holy in body and spirit; but the married woman is anxious about worldly affairs, how to please her husband. (1 Cor 7.32-34)
Yet commitments are frequently demanded of us (by friends, institutions, marriage, nation, etc), so what are we to do? If we make these commitments, we end up with divided interests, trying to obey a number of different authorities, each with their own agenda. But if we refuse to these commitments, we seem to be individualists, without a deep concern for or connection to others.
For followers of Jesus there is only one answer, the answer he gave: "You shall love the Lord your God with all your heart, and with all your soul, and with all your mind, and with all your strength." Our single, whole-hearted commitment must be to God. There can be no other loyalty or authority for us.
Yet this undivided, exclusive commitment to God does not cut us off from others. Because the commitment to God is the commitment to love.