For when something went right and you want to say so at length. It is the Church's prayer for victories, elections, coronations and the last night of the year — and it is the only thing on this site that thanks God for a full two minutes without asking for anything until the end.
It does the thing the Glory Be does, at length. Angels, apostles, prophets, martyrs, the whole Church — the first half is a roll-call of everyone praising, and you join the end of the line. The middle turns to Christ and tells his story in five sentences. Only then, and briefly, does it ask: help thy servants, keep us this day without sin, have mercy.
And it ends on one line in the first person, after all that crowd: in thee have I trusted; let me never be confounded. The whole Church has been singing, and then it is just you.
The story everybody tells is that at Augustine's baptism in Milan in 387, he and Ambrose began singing it to each other, line by line, making it up as they went. It is a lovely story and it is a legend; nothing before the eighth century says so, and the Latin is not Ambrose's.
What can be said is that it is very old — Benedict was ordering it sung at Sunday Vigils by about 530, so it was already standard — and that since 1894 most scholars have thought it was written by Nicetas of Remesiana, a bishop in what is now Serbia, around the year 400. That is likely and it is not proved. The prayer has been the Church's for sixteen hundred years and nobody's in particular.
It became the sound of something having gone right. It is sung after a pope is elected, at coronations, after victories — Rome sang it after Lepanto — and at the end of every year on the thirty-first of December, which is the one occasion most laypeople have heard it. Handel, Berlioz and Bruckner set it; the hymn Holy God, we praise thy name is a loose paraphrase, and if you know that you already know the shape of this.
On this site it is nearly alone. The needs-first catalog is built around trouble, because that is what people arrive with; this is the prayer for the day the trouble ended.