When it is said
The priest reads the third kneeling prayer at Vespers on the day of Pentecost, after the deacon calls everyone to their knees.
Anyone might pray its closing lines at home for someone who has died.
Where it comes from
Author by tradition
The first kneeling since Easter
Orthodox Christians do not kneel in church from Easter until Pentecost. Following the first Council of Nicaea, they do not kneel on Sundays either. At Vespers on the day of Pentecost they kneel for the first time since Easter, while three long prayers are read.
Church of the Mother of God, Mays Landing; N. R. Antonov, quoted by Azbyka
A prayer for those in hades
Earlier in the prayer the Church calls on Christ as the One Who went down into hades (the place of the dead), broke its bars and showed a way up to those below. Just before these closing lines it says that on this feast He accepts prayers for those held in hades, and gives us great hope that relief will be sent down to them. Then it asks rest for those who have fallen asleep.
The Greek text (glt.goarch.org); Hapgood, Service Book (1906)
The Scripture in it
It is not the dead who praise the LORD, nor any who descend into silence. But it is we who will bless the LORD, both now and forevermore. Hallelujah!
For there is no mention of You in death; who can praise You from Sheol?
So the redeemed of the LORD will return and enter Zion with singing, crowned with everlasting joy. Gladness and joy will overtake them, and sorrow and sighing will flee.
Bible text: Berean Standard Bible, public domain.
In Greek
Ἐπάκουσον ἡμῶν τῶν ταπεινῶν, οἰκτρῶν δεομένων σου,
καὶ ἀνάπαυσον τὰς ψυχὰς τῶν δούλων σου τῶν προκεκοιμημένων,
ἐν τόπῳ φωτεινῷ, ἐν τόπῳ χλοερῷ, ἐν τόπῳ ἀναψύξεως,
ἔνθα ἀπέδρα πᾶσα ὀδύνη, λύπη, καὶ στεναγμός,
καὶ κατάταξον τὰ πνεύματα αὐτῶν ἐν σκηναῖς Δικαίων,
καὶ εἰρήνης καὶ ἀνέσεως ἀξίωσον αὐτούς,
ὅτι οὐχ οἱ νεκροὶ αἰνέσουσί σε, Κύριε,
οὐδὲ οἱ ἐν ᾍδῃ ἐξομολόγησιν παρρησιάζονται προσφέρειν σοι,
ἀλλ' ἡμεῖς οἱ ζῶντες εὐλογοῦμέν σε καὶ ἱκετεύομεν,
καὶ τὰς ἱλαστηρίους εὐχὰς καὶ θυσίας προσάγομέν σοι ὑπὲρ τῶν ψυχῶν αὐτῶν.