“[The] three premises to ‘auteur’ theory: the technical competence of the director, the director’s distinguishable personality and interior meaning. He says that three concentric circles can represent the three premises, of which the outer one represents technique, the middle one – individual style and the inner one – interior meaning. The director’s interrelated roles can be designated as the roles of the technician, stylist (metteur en scene) and the ‘auteur’ respectively.” (Sarris)

The development of auteur theory is very closely linked to the emergence of the French New Wave, and particularly to the thoughts of Francois Truffaut, best expressed in his essay "A Certain Tendency of French Cinema." Further details here.

It can be further understood by reading Andrew Sarris essay which breaks it into three helpful areas.

Finally, understand that it is a controversial idea which many people disagree with - most famously, Pauline Kael, in her essay Circles and Squares (explanation here!)