HIS chapter presents the record of 2 rather intimate conversations between Christ and 2 of His disciples. John 13:1-17 tells us about Jesus washing His disciples' feet, particularly Peter's feet. John 13:32-38 focuses on Peter as well. In both cases Peter gets special attention in the story, not so much due to the intentions of Christ, but due to Peter's impetuous responses. In other words, not all the attention directed at Peter is positive (vs. 38). And, John 13:18-31 reveals the awful demise of Judas & his betrayal of the Messiah; the Savior of the world.
Truly though, Jesus is (appropriately) the real focal point of this section. Peter and Judas are good examples of sinners, but the Savior is central. Jesus celebrated His last Passover meal with His disciples; those He loved so deeply (John 13:1). After that meal, Jesus served these men (including Judas) by washing their feet. What a scene; the Creator washing the feet of His creatures (John 13:4)! Of course, Peter famously resisted Jesus' ministry (John 13:8). Perhaps Peter's reasons were at least partially wholesome, but Jesus had some other things in mind; namely, He was teaching humility (and ministry) by example (John 13:14). Beyond that, Jesus also taught us some things about salvation and sanctification (John 13:10, 13-15 & 17).