At the very Beginning of the service of Orthros (Matins) the Typicon prescribes the reading of the “Six Psalms,” or “Hexapsalm” i.e. Psalms 3, 37, 62, 87, 102, and 142, read in that order, and combined into a single whole.
The faithful should be aware of the fact that the reading of the “Six Psalms” is one of the most important points in the service , a time when all should put aside other thoughts, stand quietly, and concentrate on these penitential prayers. The reading does not constitute a pause in Divine Services, a time during which to go for a walk outside or to talk to one’s neighbor. It is one of the holiest moments in the entire service.
The Six Psalms comprise an entire scale of experiences which illumine the Christian life of the New Testament – not merely its overall joyous mood, but also the sorrowful path to that joy.
This is why according to the rubrics of the Church, the candles in the church are to be extinguished. The falling darkness symbolizes that dead of night during which Christ, praised in the angelic song “Glory to God in the Highest,” came to earth. The semi-darkness of the church facilitates great prayerful concentration.
In his reference book The New Testament, or Explanations of the Church, the Liturgy, and of all Church Services and Furnishings, published in St. Petersburg in 1908, Archbishop Benjamin of Nizhegorod and Arzamas explains the extinguishing of candles during the Six Psalms in this way: “According to the ustav (Typicon in Greek practice) , during this reading the candles are to be extinguished. This is done so that we, able to see nothing with our eyes, might listen to the Six Psalms attentively and with fear [of God] and so that everyone standing in the dark might shed a tear and release a tender sigh. For at night, and if there is no lighted candle nearby, it is difficult for people to see one another. It is for this reason that the ustav (Typicon) directs: thus we pronounce the Six Psalms with all attentiveness and fear of God, as conversing with our invisible Christ God Himself, and praying over our sins.”
Midway through the Six Psalms, at the beginning of the 4th of the psalms, the one most filled with sorrow and extreme bitterness, the priest leaves the Altar and, standing before the Royal Doors, continues to quietly read the 12 appointed morning prayers. At that point, the priest symbolizes Christ, who, having heard the sorrow of fallen mankind, not only descended, but to the very end also shared in the suffering of which Psalm 87 speaks.
The morning prayers quietly read by the priest include prayers for the Christians standing in the church, with requests that they be forgiven their sins, that they be given true faith and sincere love, that all of their works be blessed, and that they be made worthy of the Kingdom of Heaven.
Adapted from http://www.stjohndc.org/Russian/what/e_SixPsalms.htm
See bellow a link to the Six psalms as read during Orthros: