Jesus did it and told us to do it.
According to St. John’s Gospel, Jesus washed the feet of his disciples after supper on the night he was arrested. He told them that If I, your master, have washed your feet, you should also wash one another’s feet. I have given you an example (Jn.13:14,15). This passage forms the Gospel at the Mass of the Lord’s Supper on Holy Thursday evening.
In Jesus’ day, washing feet was a slave’s job. We might read St. Paul’s words He emptied himself, taking the form of a slave, being born in human likeness (Phil.2:7) as a commentary on this passage. This is one of God’s ‘mighty acts’ of salvation.
The Rite of washing of feet in our liturgy may have originated in monastic communities, though St. Ambrose records that he was accustomed to wash the feet of those whom he had just baptised and chrismated at Easter.
Since the revisions of the Holy Week Liturgy in the 1950’s and after Vatican II, the ceremony of washing of feet has been an optional part of the Mass of the Lord’s Supper, celebrated after the Homily.
The rule was that twelve men should have their feet washed by the priest. Many places expanded on that rule. More recently the rule has been relaxed, and both men and women may have their feet washed.
The ‘Twelve men’ rule made this rite a sort of historical pageant of the Gospel. The more relaxed practice has more of a ‘sacramental’ feel about it and embodies the narrative of humility and mutual service enshrined in the Gospel reading of the Mass.