In The Companion to the Book of Common Worship, by Peter Bower (credit to Wikipedia for helping me find this!), the day is explained:
Maundy Thursday (or le mandé; Thursday of the Mandatum, Latin, commandment). The name is taken from the first few words sung at the ceremony of the washing of the feet, "I give you a new commandment" (John 13:34); also from the commandment of Christ that we should imitate His loving humility in the washing of the feet (John 13:14-17). The term mandatum (maundy), therefore, was applied to the rite of foot-washing on this day.As we reflect on the incredible sacrifice that Jesus made out of love for us, let us also reflect on him as our "Servant King". As the song by Graham Kendrick goes:
This is our God, the Servant KingHow might we follow his example of loving and sacrificial service to others today?
He calls us now to follow him
To bring our lives as daily offering
Of worship to the Servant King