Christians are often not the best example of unity. Yet this is exactly what Jesus prayed his followers would be- unified. He is not calling for an institutional unity or an organizational unity, but an organic, familial unity that recognizes the oneness between Jesus and God the Father.
The demonstration of that unity and love is part of the proof the world will have as reason to believe that Jesus is the one sent from God to save sinners. (John 17:23, John 13:34-35) In addition, Jesus prayed that his disciples would sense and see his glory- the glory that he had with the Father before the foundation of the world. To see his glory and behold our savior face to face: that is the future, eternal hope that helps us make sense of our present, temporary lives.
(click to play, right click to download)