Later in the passage, Jesus told the disciples: "Love each other. Just as I have loved you, you should love each other. Your love for one another will prove to the world that you are my disciples." John 13:34-35
Little did they know the extent of what that meant. Jesus had just washed the feet of the man who would betray him to his death. His undeserved, sacrificial death... the death that he willingly went to, 'as a lamb to the slaughter'... out of... love.
What love is this? How amazing. How perfect, and pure is this love. That Jesus, the God-man, the Holy Son of God, the King of Heavens Armies-- Would not only wash the feet of, but die- a brutal, torturous death- for who? A betrayer. For who? A sinner. For who? For me.
And we, his children, are supposed to love... like this? Yes. How? Only by the grace of Jesus Christ, and the power of the Holy Spirit! Look at how Jesus loved his disciples-- look at how he has loved US! With amazing, self-sacrificing, unconditional, unassuming, immeasurable love! That's what he wants us to do as well. To act as "little Christ's", as C.S. Lewis puts it in Mere Christianity. Think hard about what that means for you.