Michael Martin, in his entry on the Dies Irae in the Treasury of Latin Prayers, gives us this helpful summary:
Dies Irae was traditionally ascribed to Thomas of Celano (d 1260), but now is usually attributed to an unknown Franciscan of that period. The piece is based upon Zep 1:14-16, a reflection upon the final judgment. It was formerly part of the Mass of the Dead and the Office of the Dead. Today it is found in the Liturgia Horarum for the last week of Ordinary time (34th). In placing it there, the emphasis is upon the upcoming Advent season and the Second Coming of Christ. In Diocese of the United States, it is still used in the Office of the Dead and the Feast of All Souls (Nov. 2).
Many have complained about the depressing nature of the opening verses, but while the piece is certainly sobering, there is a note of hope as well later on in the hymn. Judgment, which is eternal, is indeed a fearsome prospect for us sinners, but, as Christians, we also realize we have Christ as our Savior.
The Wikipedia article tells us more:
Other images come from Revelation 20:11–15 (the book from which the world will be judged), Matthew 25:31–46 (sheep and goats, right hand, contrast between the blessed and the accursed doomed to flames), 1 Thessalonians 4:16 (trumpet), 2 Peter 3:7 (heaven and earth burnt by fire), Luke 21:26–27 ("men fainting with fear ... they will see the Son of Man coming"), etc.
From the Jewish liturgy, the prayer Unetanneh Tokef also appears to have been a source: "We shall ascribe holiness to this day, For it is awesome and terrible"; "the great trumpet is sounded", etc.
Martin considers the Dies Irae to be "One of the most famous melodies of the Gregorian Chant." Henry Hugh speaks of the "vigorous beauty of the original hymn" in his article for the New Advent Encyclopedia. The Franciscan Archive calls it "a hymn of singular awe and piety." Yet, I would imagine that few Catholics have ever heard the Dies Irae.
Part of this is surely due to the aforementioned reforms. Annibale Bugnini, in his The Reform of the Liturgy: 1948–1975 ([The Liturgical Press, 1990], Chap. 46.II.1, p. 773) explains the mind of the Consilium in charge of that task:
They got rid of texts that smacked of a negative spirituality inherited from the Middle Ages. Thus they removed such familiar and even beloved texts as the Libera me, Domine, the Dies Iræ, and others that overemphasized judgment, fear, and despair. These they replaced with texts urging Christian hope and arguably giving more effective expression to faith in the resurrection.
This I think is a shame. It is unfathomable to me that "such familiar and even beloved texts" could be so swiftly discarded. Perhaps the Dies Irae has endured since the Middle Ages and received the affection of the laity for a reason?
At any rate, I would rather not dwell on the imprudent decisions of the Consilium (it depresses me). Instead, I would like to remedy the absense of this hymn in my own small way by providing the YouTube video below. See the entry on the Dies Irae in the Treasury of Latin Prayers if you would like to follow along with the Latin (with English translation) while you listen.
"Dies Irae" means "Day of wrath." May we all be ready.