At first it seems strange that Christ would call this a new command. After all, the Old Testament instructed God's people to love their neighbors and Christ himself summarized the law as love for God and love for others. So what's new about love? What makes the command new is that because of Jesus' passion there is a new standard, a new example of love.
There was never any love like the dying love of Jesus. It is tender and sweet (13:33). It serves (13:2-17). It loves even unto death (13:1). Jesus had nothing to gain from us by loving us. There was nothing in us to draw us to him. But he loved us still, while we were yet sinners. At the Last Supper, in the garden, at his betrayal, facing the Jewish leaders, before Pontius Pilate, being scourged, carrying his cross, being nailed to the wood, breathing his dying breath, forsaken by God-he loved us.
To the end.
Love shone best and brightest at Calvary.
Christ was all anguish that I might be all joy, cast off that I might be brought in, trodden down as an enemy that I might be welcomed as a friend, surrendered to hell's worst that I might attain heaven's best, stripped that I might be clothed, wounded that I might be healed, athirst that I might drink, tormented that I might be comforted, made a shame that I might inherit glory, entered darkness that I might have eternal life.My Saviour wept that all tears might be wiped from my eyes, groaned that I might have endless song, endured all pain that I might have unfading health, bore a thorned crown that I might have a glory-diadem, bowed his head that I might uplift mine, experienced reproach that I might receive welcome, closed his eyes in death that I might gaze on unclouded brightness, expired that I might for ever live. (The Valley of Vision, "Love Lustres at Calvary")