In the Eastern Orthodox Church, Clean Monday is the Monday
before Ash Wednesday.
Clean Monday is actually the Monday before Great Lent.(Apparently that was an adaptation that my research applied to the Roman Catholic Calendar.) It is a day of strict fasting from midnight til noon. The idea is to begin Lent with a clean heart and pure intentions. The following prayer is prayed on Clean Monday, as well as the 40 days of Lent.

The Prayer of Saint Ephrem the Syrian
"O Lord and Master of my life, keep from me the spirit of indifference and discouragement, lust of power and idle chatter. [kneel/prostration]
"Instead, grant to me, Your servant, the spirit of wholeness of being, humble-mindedness, patience, and love. [kneel/prostration]
"O Lord and King, grant me the grace to be aware of my sins and not to judge my brother; for You are blessed now and ever and forever. Amen. [kneel/prostration]"