"Question authority" is a popular bumper sticker slogan which first appeared in the late 1970s, and a common graffiti slogan. It is intended to encourage people to avoid [fallacious] appeals to authority.
The origin of the phrase is sometimes attributed to Timothy Leary. Enlightenment polymath Benjamin Franklin was often quoted as saying "it is the first responsibility of every citizen to question authority".
The term can also be read humorously as a noun phrase signifying "someone who is an authority on the subject of questions".