The Auteur Theory states that the best films have the imprint of an auteur (or author).
The man who coined the phrase "la politique des auteurs" in the 1950s --Francois Truffaut-- explained that the worst of Jean Renoir's movies would always be more interesting than the best of Jean Delannoy's. He and his colleagues at the magazine Cahiers du Cinema recognized that moviemaking was an industrial process. But they proposed an ideal to strive for: using the commercial apparatus just the way a writer uses a pen. And so they valued the work of those who neared this ideal.
These critics -- Truffaut, Godard, Chabrol, Rohmer--wrote mostly about directors, although they also produced some shrewd appreciations of actors. Later writers of the same general school have emphasized the contributions of star personalities like Mae West.
However, the stress was on directors, and it seemed arbitrary to many. When Andrew Sarris spread these ideas to the United States, he aggravated the problem by calling auteurism a 'theory,' as though it were an explanation of how films are made.
Screenwriters, producers and others reacted with a good deal of hostility.
But "politique" should probably have been translated as 'policy'; it involves a decision to look at movies in a certain way and to value them in a certain way. Truffaut provocatively said, "There are no good and bad movies, only good and bad directors." What he meant was that art can't be arrived at by some quality-control process -- finding an 'important' subject, hiring a 'distinguished' playwright, finding 'authentic' locations, and so on. A movie might fail in many ways and still be important as a revelation of what some creator thinks and feels.