A mode is a musical scale which does not conform to the behavior of a typical Western major or minor key. The term can refer to one of three different types of scales:
The so-called "church modes" were named after ancient Greek scales, or topoi, with the names "Lydian," "Dorian," "Phrygian," and "Mixolydian." Four more modes were modified versions of these, adding the prefix "hypo" (i.e. "Hypophrygian"). Despite their sharing names with the topoi, their interval content has nothing to do with the ancient Greek scales, the sound of which would have been unknown to the 9th century theorists who gave the modes these names.
Modern modal usage is based on some of the same names as the church modes, but also with some significant differences. One can easily understand the concept of modes by imagining a C-major scale, and by playing a new scale with the same notes, but beginning on each successive member of the scale. Beginning on C, the modes are named:
C - Ionian (CDEFGABC)
D - Dorian (DEFGABCD)
E - Phrygian (EFGABCDE)
F - Lydian (FGABCDEF)
G - Mixolydian (GABCDEFG)
A - Aeolian (ABCDEFGA)
B - Locrian (BCDEFGAB)
Any of the modes can of course be transposed to begin on any of the twelve pitches.
The Locrian mode, because of the unstable diminished interval between its root and fifth, is very seldom used as a the main mode of a piece. It is, however, used in modal jazz.
In the modern usage of modes, especially in jazz, there is usually also an avoidance of typical rules of classical harmony. Therefore, the Ionian and the Aeolian modes, while being in principle the same as the major and minor scales, will reflect this semantic difference. Often, this includes the avoidance of chords and chord progressions altogether.
There is yet another meaning of mode in music which has nothing to do with a scale. It also describes certain rhythmic practices in 13th and 14th century music. The difference is usually made clear by referring to this usage as "Rhythmic Mode."
Donald J. Grout and Claude Palisca, Norton History of Western Music.