Subsets of the chromatic scale of twelve notes, these modes are made up of several symmetrical groups, the last note of each group being the first note of the next. After a certain number of chromatic transpositions (i.e. up or down a semitone) each mode cannot be transposed further - the next transposition resulting in exactly the same notes as the first.
For example, the first mode contains notes C, D, E, F#, G#, A#, C; transposing this mode up a semitone gives C#, D#, F, G, A, B, C#. Transposing this up another semitone would give D, E, F#, G#, A#, C, D which is exactly the same set of notes we started with.
Messiaen found ways of employing all of these modes both harmonically and melodically.
The second mode, also called octatonic scale, is divided into four groups of three notes each. It has three transpositions, like the diminished-seventh chord. Here it is, expressed melodically:
The third mode is divided into three groups of four notes each. It has four transpositions, like the augmented triad. Here it is, expressed melodically:
Here are the fourth, fifth, sixth and seventh modes. They each have six transpositions, like the tritone.