The use of the Gradual Psalms is truly ancient: Psalms 119-133 are clearly identified as a group in the Old Testament, and labelled as such, and the Church's tradition is that Our Lady recited them.
The law and the ascent of grace
In Scripture, they are immediately preceded by Psalm 118’s extended meditation on the law of the Lord.
The implicit message, I think, is that first we must build the foundations for grace, which are the law, on which the happy man meditates day and night, for only after we have a sound grounding in the law can we set of the spiritual ascent to which the psalms invite us.
Pilgrim songs or liturgical hymns?
These psalms are thought to have been sung liturgically as the pilgrims ascended the fifteen steps of the Temple in Jerusalem on major feasts.
These psalms can also be viewed as pilgrim songs, appropriate perhaps for Christ's wanderings around the region as he preached.
But above all, the Fathers saw them as tracing the mystical ascent of the Christian in the spiritual life in imitation of Christ, who shows us how to climb Jacob’s ladder to heaven and grow in virtue.
St John Chrysostom for examples opens his discussion on the set by saying:
"While to each of the other psalms belongs its own title, in this case a collection of a number of them took one name A Song of the Steps, which a different translator called "the Ascents" as opposed to some who call them "Steps." Why, do you ask, are they so called? In a historical sense, because they tell of the return from Babylon and mention the captivity there; in a spiritual sense, because they give guidance to the way of virtue, as some interpret them. The way that leads there, you see, is like steps, gradually guiding the man of virtue and sound values, and placing him in heaven itself. Others, on the contrary, claim there is reference in this to the ladder of Jacob, which was revealed to him reaching up to heaven."
In the New Testament
The first of the group, Psalm 119, presents us with the image of an exile, a stranger living amongst antagonistic peoples, who has ‘lived too long in exile’. Hebrews 11 nicely summarises the storyline that then develops:
“These all died in faith…having acknowledged that they were strangers and exiles on the earth. For people who speak thus make it clear that they are seeking a homeland. If they had been thinking of that land from which they had gone out, they would have had opportunity to return. But as it is, they desire a better country, that is, a heavenly one. Therefore God is not ashamed to be called their God, for he has prepared for them a city.”
Hebrews contrasts the story of the Old Testament figures who set out on this journey, but were not able to arrive at the destination because heaven was closed to them by Original Sin, with our situation, whereby the gates to heaven have been reopened by our Lord. But it also points to the key orientation of the Christian: living in the world, but not being of it; and focusing on laying up treasure in heaven, not in the here and now:
"Why then, since we are watched from above by such a cloud of witnesses, let us rid ourselves of all that weighs us down, of the sinful habit that clings so closely, and run, with all endurance, the race for which we are entered. Let us fix our eyes on Jesus, the origin and the crown of all faith, who, to win his prize of blessedness, endured the cross and made light of its shame, Jesus, who now sits on the right of God’s throne." (Hebrews 12)
Indeed, Christ is the 'third temple', as St John's Gospel asserts in a text that many of the Fathers regarded as the key to the interpretation to the Gradual psalms:
"Jesus answered them, Destroy this temple, and in three days I will raise it up again. At which the Jews said, This temple took forty-six years to build; wilt thou raise it up in three days? But the temple he was speaking of was his own body; and when he had risen from the dead his disciples remembered his saying this, and learned to believe in the scriptures, and in the words Jesus had spoken." (John 2: 19-22).