The first eight modes were designated in the medieval era, as a way to classify pre-existing Gregorian chants. The next four were added by Glareanus in 1547. This gave way to our modern system of tonality, especially via the Ionian mode.
The most important note of a mode is its "final" or the note on which it cadences. This is important to mention for these brief descriptions, because the modes come in authentic and plagal pairs. In the authentic modes, the final is the lowest note of the mode's scale, whereas in the plagal modes, the final is the fourth note. The finals will be emphasized typographically below.
Convenviently, the scales for these modes are easily represented (aside from issues of tuning) by the white keys on the modern piano, simply by starting from different notes. Today they are sometimes called "the mode on D" etc.