From: John 13:31-33a, 34-35
The New Commandment
 When he (Judas Iscariot) had gone out, Jesus said, "Now is the Son of Man glorified, and in Him God is glorified;  if God is glorified in Him, God will also glorify Him in Himself, and glorify Him at once.  Little children, yet a little while I am with you.  A new commandment I give you, that you love one another; even as I have loved you, that you also love one another.  By this all men will know that you are My disciples, if you love one another."
31-32. This glorification refers above all to the glory which Christ will receive once He is raised up on the cross (John 3:14; 12:32). St. John stresses that Christ's death is the beginning of His victory: His very crucifixion can be considered the first step in His ascension to His Father. At the same time it is glorification of the Father, because Christ, by voluntarily accepting death out of love, as a supreme act of obedience to the Will of God, performs the greatest sacrifice man can offer for the glorification of God. The Father will respond to this glorification which Christ offers Him by glorifying Christ as Son of Man, that is, in His holy human nature, through the His resurrection and ascension to God's right hand. Thus the glory which the Son gives the Father is at the same time glory for the Son.
Christ's disciple will also find His highest motivation by identifying himself with Christ's obedience. St. Paul teaches this very clearly when he says: "Far be it from me to glory except in the cross of the Lord Jesus Christ" (Galatians 6:14).
33. From this verse onwards the evangelist recounts what is usually called the discourse of the Last Supper; in it we can distinguish three parts. In the first, our Lord begins by proclaiming the New Commandment (verses 33-35) and predicts Peter's denials (verses 36-38); He tells them that His death means His going to the Father (Chapter 4), with Whom He is one because He is God (verses 1-14); and He announces that after His resurrection He will send them the Holy Spirit, who will guide them by teaching them and reminding them of everything He told them (verses 15-31).
The second part of the discourse is contained in Chapters 15 and 16. Jesus promises to those who believe in Him a new life of union with Him, as intimate as that of a vine and its branches (15:1-18). To attain this union one must keep His New Commandment (verses 9-18). He forewarns them about the contradictions they will suffer, and He encourages them by promising the Holy Spirit who will protect them and console them (verses 18-27). The action of the Paraclete or Consoler will lead them to fulfill the mission Jesus has entrusted to them (16:1-15). The fruit of the presence of the Holy Spirit will be fullness of joy (verses 16-33).
The third part (Chapter 7) gives Jesus' priestly prayer, in which He asks the Father to glorify Him through the cross (verses 1-5). He prays also for His disciples (verses 6-19) and for all those who through them will believe in Him, so that, staying in the world without being of the world, the love of God should be in them and they should bear witness to Christ being the envoy of the Father (verses 20-26).
34-35. After announcing that He is leaving them (verse 33), Christ summarizes His commandments in one--the New Commandment. He will repeat it a number of times during the discourse of the Supper (cf. John 15:12, 17), and St. John in his First Letter will insist on the need to practice this commandment of the Lord and on the demands it implies (cf. 1 John 2:8; 3:7-21).
Love of neighbor was already commanded in the Old Testament (cf. Leviticus 19:18)--and Jesus ratified this when He specified that it was the second precept of the whole Law and similar to the first: Love God will all your heart and soul and mind (cf. Matthew 22:37-40). But Jesus gives the precept of brotherly love new meaning and content by saying "even as I have loved you". The love of neighbor called for by the Old Law did also in some way extend to one's enemies (Exodus 23:4-5); however, the love which Jesus preaches is much more demanding and includes returning good for evil (cf. Matthew 5:43-44), because Christian love is measured not by man's heart but by the heart of Christ, who gives up His life on the cross to redeem all men (cf. 1 John 4:9-11). Here lies the novelty of Jesus' teaching, and our Lord can rightly say that it is His commandment, the principal clause in His last will and testament.
Love of neighbor cannot be separated from love of God: "The greatest commandment of the law is to love God with one's whole heart and one's neighbor as oneself (cf. Matthew 22:37-40). Christ has made this love of neighbor His personal commandment and has enriched it with a new meaning when He willed Himself, along with His brothers, to be the object of this charity, saying: `As you did it to one of the least of these My brethren, you did it to Me' (Matthew 25:40). In assuming human nature He has united to Himself all humanity in a supernatural solidarity which makes of it one single family. He has made charity the distinguishing mark of His disciples, in the words: `By this all men will know that you are My disciples, if you have love for one another'" (Vatican II, "Apostolicam Actuositatem", 8).
Even though Christ is Purity itself, and Temperance and Humility, He does not, however, make any one of these virtues the distinguishing mark of His disciples: He makes Charity that mark. "The Master's message and example are clear and precise. He confirmed His teaching with deeds. Yet I have often thought that, after twenty centuries, it is indeed still a NEW commandment, for very few people have taken the trouble to practice it. The others, the majority of men, both in the past and still today, have chosen to ignore it. Their selfishness has led them to the conclusion: `Why should I complicate my life? I have more than enough to do just looking after myself.'
"Such an attitude is not good enough for us Christians. If we profess the same faith and are really eager to follow in the clear footprints left by Christ when He walked on this earth, we cannot be content merely with avoiding doing unto others the evil that we would not have them do unto us. That is a lot, but it is still very little when we consider that our love is to be measured in terms of Jesus' own conduct. Besides, he does not give us this standard as a distant target, as a crowning point of a whole lifetime of struggle. It is--it ought to be, I repeat, so that you may turn it into specific resolutions--our starting point, for our Lord presents it as a sign of Christianity: `By this shall all men know that you are My disciples'" ([St] J. Escriva, "Friends of God", 223).
And this is what in fact happened among Christians in the early centuries in the midst of pagan society, so much so that Tertullian, writing around the end of the second century, reported that people could indeed say, looking at the way these Christians lived: "See how they love one another" ("Apologeticum", XXXIX).
Source: "The Navarre Bible: Text and Commentaries". Biblical text taken from the Revised Standard Version and New Vulgate. Commentaries made by members of the Faculty of Theology of the University of Navarre, Spain. Published by Four Courts Press, Kill Lane, Blackrock, Co. Dublin, Ireland. Reprinted with permission from Four Courts Press and Scepter Publishers, the U.S. publisher.