The term used by commentators to describe the style of composition initiated by Schoenberg and his students beginning around 1908, in which no particular tonal centricity is in evidence, all 12 tones of the 12-edo chromatic scale being used freely.
Schoenberg himself detested the use of "atonal" to describe this music, preferring to call it "pantonal". However, "pantonal" never gained much currency and "atonal" has become the standard term to describe music without a tonal center. This style became quite popular with composers of "serious" music during the 20th century, and also extended into jazz during the 1960s.
Ivor Darreg pointed out that composers who really wished to write truly atonal music would have done well to adopt 11-edo or 13-edo, as those tunings do a far worse job of approximating familiar 3-limit and 5-limit intervals than does 12-edo. Schoenberg's explicit intent was to have 12-edo approximate the less familiar ratios of 11 and 13, which it emphatically does not do well.