The triduum begins with the evening Mass of the Lord's Supper on Holy Thursday, which commemorates when Jesus instituted the Eucharist at the Last Supper.
The traditional English name for this day, "Maundy Thursday," comes from the Latin phrase mandatum novum -- "a new command" (or mandate) -- which comes from Christ's words: "I give you a new commandment: Love one another. As I have loved you, so you also should love one another" (Jn 13:34). The Gospel reading for the liturgy is from the first part of the same chapter and depicts Jesus washing the feet of the disciples, an act of servitude (commonly done by slaves or servants in ancient cultures) and great humility.
Earlier on Holy Thursday (or earlier in the week) the bishop celebrates the Chrism Mass, which focuses on the ordained priesthood and the public renewal by priests of their promises to faithfully fulfill their office.
In the evening liturgy, the priest, who is persona Christi, will wash the feet of several parishioners, oftentimes catechumens and candidates who will be entering into full communion with the Church at Easter Vigil. In this way the many connections between the Eucharist, salvation, self-sacrifice and service to others are brought together.
These realities are further anticipated in Jesus' remark about the approaching betrayal by Judas: "Whoever has bathed has no need except to have his feet washed, for he is clean all over; so you are clean, but not all" (Jn 13:10-11). The sacrificial nature of the Eucharist is brought out in the Old Testament reading, from Exodus 12, which recounts the first Passover and God's command for the people of Israel, enslaved in Egypt, to kill a perfect lamb, eat it and then spread its blood over the door as a sign of fidelity to the one, true God.
Likewise, the reading from Paul's epistle to the Christians in Corinth (1 Cor 11:23-26) repeats the words given by the Son of God to his apostles at the Last Supper: "This is my body that is for you. Do this in remembrance of me" and "This cup is the new covenant in my blood. Do this, as often as you drink it, in remembrance of me."
Thus, in this memorial of Jesus' last meal with his disciples, the faithful are reminded of the everlasting value of that meal, the gift of the priesthood, the grave dangers of turning away from God, the necessity of the approaching cross and the abiding love that the Lord has for his people.