Using reverent and apocalyptic language, "Holy, Holy, Holy!" alludes to Revelation 4:6-11; 5:13; 15:2-4; and Isaiah 6:1-3 to sing the great majesty of the triune God. Note the cosmic scope of the text: human beings (st. 1), saints and angels in glory (st. 2), and all creation (st. 4) praise the name of the Lord! Though God's holiness, love, and purity are cloaked in mystery, we can still experience God's mercy and mighty power, and we can participate in praising God. The text is trinitarian in theme, but not in structure.
Bert Polman, Psalter Hymnal Handbook
God’s children are called to and gathered to give worship to all three members of the Trinity. Belgic Confession, Article 8, gives the clearest explanation of the three persons of the Trinity, including not only their identity, but also their nature and tasks: “The Father is the cause, origin, and source of all things, visible and invisible. The Son is the Word, the Wisdom, and the image of the Father. The Holy Spirit is the eternal power and might, proceeding from the Father and the Son.”
Heidelberg Catechism, Lord’s Day 8, Questions and Answers 24 and 25 does so in much briefer form. As does the Belhar Confession, Section 1: “We believe in the triune God, Father, Son and Holy Spirit, who gathers, protects and cares for the church through Word and Spirit. This, God has done since the beginning of the world and will do to the end.”