Excerpted from the Handbook for Church Servers of Sergei Bulgakov:
In the services for this Sunday the Holy Church glorifies the holy cross and the fruits of the death of the Savior on the cross. She will carry out the holy cross into the middle of the temple for veneration, and is why the Sunday is called the Veneration of the Cross...
The purpose of instituting the Holy Cross in the service on the third Sunday will be revealed as a beautiful comparison by the Holy Church to the tree of life in paradise, the tree which sweetened the bitter waters of Marah, the tree with the canopy of leaves under whose shade tired travelers seeking the eternal promised land may find coolness and rest. Thus, the Holy Church offers the Holy Cross for spiritual reinforcement to those going through the ascetic effort of the fast, just as food, drink and rest serve as bodily reinforcement. This spiritual reinforcement is given as the representation of the love of God to man for whom the Son of God turned Himself over to death on the cross. It is especially necessary in the middle of our effort because now our ascetic efforts already have lost much of the freshness of its power and however yet cannot hopefully enliven itself for the near and successful ending of our ascetical effort. Having concentrated all that is the most severe and sorrowful in the worship services of the previous weeks, especially during the first, that may both frighten the sinner and apparently touch the hardest of human hearts, now in the middle of the large and difficult arena of the Holy Forty Day Fast the Holy Church offers the Holy Cross for great comfort and encouragement as needed for raising the flagging strength of those fasting. Wherefore nothing can both console, encourage, and inspire the fatigued, or perhaps even the Christian weakened in spirit so much as the presentation of the eternal divine love of the Savior who turned Himself over to the struggle on the cross for the sake of our salvation.
For such a purpose the Holy Church offers the cross on the third Sunday of Great Lent from of old. Many hymns of praise for this Sunday were composed by Joseph and Theodore of the Studite Monastery. Everything in the worship service of this day: the most Holy Cross, solemnly carried from the altar to the middle of the temple, the singing of the stichera for venerating the cross, the Epistle, recounting the suffering of the Savior on the cross as the means of our reconcilement with God, the Gospel, reminding the Christian about everyone’s duty to bear their cross in life, following the Crucified One on the cross, - everything that promotes the deep stamp of the cross of Christ on the heart of the believer, as a sign of our salvation, as our mighty, God-given power, saving us on earth and opening to us the entrance to the high place of our fatherland, as the highest and more powerful reinforcement of believers among the ascetics of the Holy Forty Day Fast. If the Lord suffered on a cross for our sake then we also should practice asceticism unceasingly in fasting, prayer and other efforts of piety for His sake, discharging from ourselves and destroying in ourselves all that interferes with these efforts. With the aim of our greater enthusiasm for patience in efforts of piety, the Holy Church on the present day comfortably reminds us beforehand about coming nearer "to the light of the peaceful joy of Pascha", hymning, in the troparia of the canon, the holy cross and the suffering of the Savior on it, together with His joyful resurrection and inviting the faithful "with pure mouths" to sing "the song of joyfulness" - Irmos of Holy Pascha.
From the Lenten Triodion:
To destroy the curse of Adam, Thou dost assume our flesh, free from the stain of sin; and in Thy surpassing love, O Jesus, Thou art crucified and slain. Therefore we venerate in faith Thy Cross, the spear, the sponge, the reed and nails, and we pray to see Thy Resurrection.
As we celebrate today the joyful veneration of Thy life-giving Cross, O Christ our Saviour, we prepare ourselves for Thy most holy Passion; for Thou in Thine almighty power hast brought to pass the salvation of the world.
Cleansed by abstinence let us draw near, and with fervent praise let us venerate the all-holy Wood on which Christ was crucified when He saved the world in His compassion.
Thy Cross, O Lord all-merciful, is honoured by the whole world, for Thou hast made the instrument of death into a source of life. Sanctify those who venerate it, O God of our fathers, who alone art blessed and greatly glorified.
Seeing the Precious Cross of Christ placed this day before us, let us venerate it and rejoice in faith; with love let us greet the Lord who by His own free choice was crucified upon it, asking Him to grant us all uncondemned to adore His Holy Passion and to attain the Resurrection.