The hours are 10 minute prayer services appointed by the Church for certain hours of the day. While most of us do not generally have time to pray these prayers regularly, they are a valuable resource for reflection and prayer.
The sixth hour is the prayer appointed for noontime. This is a time when many of us may be able to set aside five minutes for reflection, reading and prayer. It is also a time when we can be prone to despondency or depression, which the fathers call "the demon of noonday." In the morning, we may have awoken with high hopes for the day. Reading our morning prayers, we gave glory to God for a new day and asked to be guided on the path of his commandments. But since then we have been exposed to numerous temptations, and are probably conscious of a number of sins. The prayers of the sixth hour reflect this struggle, and they also remind us that the answer, the solution, is to hope in God. In the words of Psalm 90, "thou shalt not be afraid for the terror by night, nor for the arrow that flieth by day. Nor for the thing that walketh in darkness, nor for the mishap and demon of noonday."
We also read the sixth hour in church just before the Divine Liturgy every Sunday. We also read the third hour (the church's mid-morning prayer) at that time.
Give ear, O God, unto my prayer, and disdain not my supplication; attend unto me, and hear me. I was grieved in my meditation, and I was troubled at the voice of the enemy and at the oppression of the sinner; Because they have turned iniquity upon me, and with wrath were they angry against me. My heart is troubled within me, and the terror of death is fallen upon me. Fear and trembling are come upon me, and darkness hath covered me. And I said: Who will give me wings like a dove? And I will fly, and be at rest. Lo, I have fled afar off and have dwelt in the wilderness. I waited for God that saveth me from faintheartedness and from tempest. Plunge them into the depths, O Lord, and divide their tongues, for I have seen iniquity and gainsaying in the city. Day and night they go round about her upon her walls; iniquity and toil and unrighteousness are in the midst of her. And usury and deceit have not departed from her streets. For if mine enemy had reviled me, I might have endured it. And if he that hateth me had spoken boastful words against me, I might have hid myself from him. But thou it was, O man of like soul with me, my guide and my familiar friend, Thou who together with me didst sweeten my repasts; in the house of God I walked with thee in oneness of mind. Let death come upon such ones, and let them go down alive into hades. For wickedness is in their dwellings, and in the midst of them. As for me, unto God have I cried, and the Lord hearkened unto me. Evening, morning, and noonday will I tell of it and will declare it, and He will hear my voice. He will redeem my soul in peace from them that draw nigh unto me, for they among many were with me. God will hear, and He will humble them, He that is before the ages. For to them there is no requital, because they have not feared God; He hath stretched forth His hand in retribution. They have defiled His covenant; they were scattered by the wrath of His countenance, and their hearts have convened. Their words were smoother than oil, and yet they are darts. Cast thy care upon the Lord, and He will nourish thee; He will never permit the righteous to be shaken. But Thou, O God, shalt bring those men down into the pit of destruction. Bloody and deceitful men shall not live out half their days; but as for me, O Lord, I will hope in Thee.
He that dwelleth in the help of the Most High shall abide in the shelter of the God of heaven. He shall say unto the Lord: Thou art my helper and my refuge. He is my God, and I will hope in Him. For He shall deliver thee from the snare of the hunters and from every troubling word. With His shoulders shall He overshadow thee, and under His wings shalt thou have hope. With a shield will His truth encompass thee; thou shalt not be afraid for the terror by night, nor for the arrow that flieth by day. Nor for the thing that walketh in darkness, nor for the mishap and demon of noonday. A thousand shall fall at thy side, and ten thousands at thy right hand, but unto thee shall it not come nigh. Only with thine eyes shalt thou behold, and thou shalt see the reward of sinners. For Thou, O Lord, art my hope. Thou madest the Most High thy refuge; No evils shall come nigh unto thee, and no scourge shall draw nigh unto thy dwelling. For He shall give His angels charge over thee, to keep thee in all thy ways. On their hands shall they bear thee up, lest at any time thou dash thy foot against a stone. Upon the asp and basilisk shalt thou tread, and thou shalt trample upon the lion and dragon. For he hath set his hope on Me, and I will deliver him; I will shelter him because he hath known my name. He shall cry unto me, and I will hearken unto him. I am with him in affliction, and I will rescue him and glorify him. With length of days will I satisfy him, and I will show him My salvation.
Seeing that we have no boldness on account of our many sins, do thou beseech Him that was born of thee, O Virgin Theotokos for the supplication of a mother availeth much to win the Master's favor. Disdain not the prayers of sinners, O all-pure one, for merciful and mighty to save is He Who deigned also to suffer for our sake.
Let Thy compassions quickly go before us, O Lord, for we are become exceedingly poor. Help us, O God our Savior, for the sake of the glory of Thy name. O Lord, deliver us and be gracious unto our sins for Thy name's sake.
Prayer of the 6th Hour, by St. Basil the Great
O God and Lord of Hosts, and Maker of all Creation, Who by the tender compassion of Thy mercy which transcendeth comprehension, didst send down Thine only-begotten Son, our Lord Jesus Christ, for the salvation of our race, and by His precious Cross didst tear asunder the handwriting of our sins, and thereby didst triumph over the principalities and powers of darkness: Do Thou Thyself, O Master, Lover of mankind, accept also from us sinners these prayers of thanksgiving and entreaty, and deliver us from every destructive and dark transgression, and from all enemies, both visible and invisible, that seek to do us evil. Nail down our flesh with the fear of Thee, and incline not our hearts unto words or thoughts of evil, but pierce our souls with longing for Thee, so that ever looking to Thee, and being guided by Thy Light as we behold Thee, the unapproachable and everlasting Light, we may send up unceasing praise and thanksgiving unto Thee, the Unoriginate Father, with Thine Only-begotten Son, and Thine All-holy and good and life-creating Spirit, now and ever, and unto the ages of ages. Amen.
The entire text can be found here: http://www.saintjonah.org/services/third&sixth.htm.
St John Cassian talks about the demon of noonday: http://hagioipateres.wordpress.com/2005/06/17/the-demon-of-the-noonday/
see also http://orthodoxwiki.org/Akedia/ While we are not a desert dweller, many of us know this demon too well.