Messiaen wrote the following explanations of each segment of the piece:

Liturgie de cristal 
Liturgy of crystal

Between the morning hours of three and four, the awakening of the birds: a thrush or a nightingale soloist improvises, amid notes of shining sound and a halo of trills that lose themselves high in the trees. Transpose this to the religious plane: you will have the harmonious silence of heaven.

Vocalise, pour l’Ange qui annonce la fin du Temps
Vocalise, for the angel who announces the end of Time

The first and third parts (very short) evoke the power of that mighty angel, his hair a rainbow and his clothing mist, who places one foot on the sea and one foot on the earth. Between these sections are the ineffable harmonies of heaven. From the piano, soft cascades of blue-orange chords, encircling with their distant carillon the plainchant-like recitativo of the violin and cello.

Abîme des oiseaux
Abyss of the birds.

Clarinet solo. The abyss is Time, with its sadnesses and tediums. The birds are the opposite of Time; they are our desire for light, for stars, for rainbows and for jubilant outpourings of song!

Intermède
Interlude

Scherzo. Of a more outgoing character than the other movements but related to them, nonetheless, by various melodic references.

Louange à l’Éternité de Jésus
Praise to the eternity of Jesus

Jesus is here considered as one with the Word. A long phrase, infinitely slow, by the cello expatiates with love and reverence on the everlastingness of the Word, mighty and dulcet, “which the years can in no way exhaust.” Majestically the melody unfolds itself at a distance both intimate and awesome. “In the beginning was the Word, and the Word was with God, and the Word was God.”

Danse de la fureur, pour les sept trompettes
Dance of fury, for the seven trumpets

Rhythmically the most idiosyncratic movement of the set. The four instruments in unison give the effect of gongs and trumpets (the first six trumpets of the Apocalypse attend various catastrophes, the trumpet of the seventh angel announces the consummation of the mystery of God). Use of extended note values, augmented or diminished rhythmic patterns, non-retrogradable rhythms – a systematic use of values which, read from left to right or from right to left, remain the same. Music of stone, formidable sonority; movement as irresistible as steel, as huge blocks of livid fury or ice-like frenzy. Listen particularly to the terrifying fortissimo of the theme in augmentation and with change of register of its different notes, toward the end of the piece.

Foullis d’arcs-en-ciel, pour l’Ange qui annonce la fin du Temps
Cluster of rainbows, for the angel who announces the end of Time

Here certain passages from the second movement return. The mighty angel appears, and in particular the rainbow that envelops him (the rainbow, symbol of peace, of wisdom, of every quiver of luminosity and sound). In my dreamings I hear and see ordered melodies and chords, familiar hues and forms; then, following this transitory stage I pass into the unreal and submit ecstatically to a vortex, a dizzying interpenetration of superhuman sounds and colors. These fiery swords, these rivers of blue-orange lava, these sudden stars: Behold the cluster, behold the rainbow!

Louange à l’Immortalité de Jésus
Praise to the immortality of Jesus

Expansive violin solo balancing the cello solo of the fifth movement. Why this second glorification? It addresses itself more specifically to the second aspect of Jesus – to Jesus the man, to the Word made flesh, raised up immortal from the dead so as to communicate His life to us. It is total love. Its slow rising to a supreme point is the ascension of man toward his God, of the Son of God toward his Father, of the mortal newly made divine toward paradise.

And I repeat anew what I said above: All this is mere striving and childish stammering if one compares it to the overwhelming grandeur of the subject!

Notes by Jessie Rothwell (Los Angeles Philharmonic)