In the Catholic tradition, every day of the week before Easter is observed as a special day. The week is called Holy Week. Maundy is a word that comes from the Latin word mandatum, meaning commandment. It is the first word of Jesus' saying: "Mandatum novum do vobis ut diligatis invicem sicut dilexi vos" or if you prefer English, "A new commandment I give unto you, That you love one another; as I have loved you". (John 13:34)
Jesus spoke these words in connection with his washing of the disciples feet before they celebrated the Lord's Supper.
Foot washing was slave work in the time of Jesus. That is why you see Peter object to Jesus washing his feet. Jesus was the master of the group, but he took on the roll of the slave by washing feet. He lived out what Paul would later say in Philippians 2. He took on the role of a servant.
Of course Jesus went on to serve us as a slave, dying on the cross to pay the penalty of our sins. Crucifixion was a penalty suffered most by slaves and also by traitors. It was a way to keep the thousands of Roman slaves in line. After the rebellion of Spartacus, for example, hundreds of slaves were crucified along the roads and left to hang there as a message to the other slaves.
Yet Jesus was obedient to the cross. And all believers, who were once slaves to sin, were redeemed by the God who died like a slave for us.
Following Christ's example, we who follow this Lord who died like a slave, can die to our own pride and ambition, and serve each other in love, even to the washing of dirty feet.