From the Sacred Triduum Missal, published by Neri Publications and Opus Mariae Mediatricis:
The rites of Maundy Thursday emphasize the institution by our Lord of the Sacrament of the Holy Eucharist, the sacrament of Holy Orders, and the Sacrifice of the Mass. The ceremony of the washing of the feet of twelve men, who represent the apostles, expresses the perfect humility of Jesus Christ shown also in the Sacrifice and Sacrament of the altar. Mention should be made of the evocative rubric which dictates that the kiss of peace not be offered in the solemn celebration of this Mass. No doubt the Church in this rubric cringes at the possibility of offering the kiss of peace, given that our Lord Jesus Christ was betrayed by a kiss. As a matter of fact it does not return, along with the accompanying prayer for peace, until Easter Sunday morning, given the fact as the Gospel reports that historically this gift of supernal peace was bequeathed by Our Lord to His disciples on Easter Sunday morning. For the same reason, the "dona nobis pacem" is omitted from the third Agnus Dei as this gift will be given us on Easter Sunday. The ceremonies of today's liturgy conclude with the procession of the Blessed Sacrament to the altar of Repose, signifying the fact that our Lord has gone into seclusion until his arrest at the hand of His enemies. Let us keep solemn watch before Our Lord until midnight and simple watch throughout the hours of Good Friday until the Mass of the Pre-Sanctified. The final ceremony is the stripping of the altar. Because the altar symbolizes Christ, having etched five crosses in honor of His five wounds, this ceremony symbolizes the stripping from Christ of His sacred garments.