August is the eighth month in the Western or Gregorian calendar; it is a proper noun and should be capitalized. It can be plural in the form of Augusts.
While much of the world uses or at least recognizes the Gregorian calendar, there are quite a few other calendars in use throughout the world. These include the Chinese, Indian, Islamic or Hijri, Coptic, Persian, Balinese, Baha’i and Jewish calendars, among others.
As an adjective, august describes something or someone as being impressive or royal. It has the derivatives of a noun form, augustness, and an adverb form, augustly.