The Hexapsalmos are a group of six psalms, composed of two triads; beginning with Psalm 3, 37, 52 and ending with Psalm 87, 102, 142. These area read after the dismissal of the Mesonyktikon or Nocturne at the beginning of the Matins service.
The monastic tradition of Mount Athos informs us that the duration it takes to read the Hexapsalmos is what they believe it will take for Christ to "judge" all of humanity at the final judgement. If a monk walks into church as the Hexapsalmos is read, they are expected to stop where they are and not move until the entire reading has been completed.
During the Hexapsalmos, the Priest comes into the holy Sanctuary, and standing before the Holy Table makes the ekphonesis with reverence and the fear of God, Blessed is our God; the Reader says the Trisagion; the Priest, the For Thine is the kingdom; the Reader, the troparia Save, O Lord, Thy people, Glory..., Thou who wast lifted up on the Cross, Both now, Awesome protection, the Priest, Have mercy on us, O God etc., the ending, For Thou art a merciful God… and the Reader, In the name of the Lord, Father, bless; the Priest, Glory to the Holy and Consubstantial…, etc., the Proïstamenos says the Hexapsalmos with compunction while the people listen in total silence and reverence.
The Hexapsalmos are never left out, save the Week of New Creation and the day of the leave-taking of Pascha.
Psalms 3 is read for the "Help for the Afflicted" Psalms 37 is a psalm of repentance. Psalm 62 Psalms 87 (is a remembrance of the Darkness of death. Psalms 102 is a praise for mercy and for the Angelic hosts. In Psalm 142 we wait in darkness for the Light.