From Wikipedia: a method of musical composition devised by Austrian composer Arnold Schoenberg (1874–1951). The technique is a means of ensuring that all 12 notes of the chromatic scale are sounded as often as one another in a piece of music while preventing the emphasis of any one note[3] through the use of tone rows, orderings of the 12 pitch classes. All 12 notes are thus given more or less equal importance, and the music avoids being in a key. The technique was influential on composers in the mid-20th century.
Schoenberg himself described the system as a "Method of composing with twelve tones which are related only with one another".[4] It is commonly considered a form of serialism.
A Super Simplified Explanation: A sequence of the 12 chromatic notes, with no repeating notes before the cycle repeats.
Examples:
[ E Ab D B Gb A F G C Eb Db Bb ]
[ C D E Eb Bb G Db B F Gb A Ab ]
[ E C B F A D Bb Ab Eb Db Gb G ]