In today's reading at Mass from Luke 14, Jesus makes it clear that one must hate all his own family members and even his own life in order to be his disciple. Obviously, "hate" is a relative term here. Jesus wants us to be attached to him alone.
To me, a detached person is one who
(1) is attached to God only and not to all else,
(2) sees that all his family members belong to God and not to him,
(3) is not cold but a true realist, seeing through God's loving eyes,
(4) lives in the present moment, looking forward to eternal life with God, and does not get overly sentimental or nostalgic,
(5) has all his priorities put in order according to God's will,
(6) is no longer a slave to himself or the world, and thus free to love God.