An auteur is a director who makes films that reflect their own personal vision, aesthetic, style, convictions, etc. Some directors, when you look at their body of work, have a pretty diverse film portfolio that don’t necessarily have to do with a specific style. For instance, a director like Robert Zemeckis makes action-adventure films (Back to the Future), dramas (Forrest Gump) and campy dark comedies (Death Becomes Her). Someone like Steven Spielberg is a jack-of-all-trades, switching easily between horror (Jaws), adventure (Indiana Jones), drama (Schindler’s List) to science fiction/fantasy (Minority Report, War of the Worlds).
Auteurs, on the other hand, tend to have their own trademarks and thematic and stylistic preferences. They also tend to be involved in every aspect of the filmmaking process, from writing to producing and designing the sets. For instance, Alfred Hitchcock is an auteur because not only is he someone who is associated with an entire genre (horror), but he also employs filmic devices that are specific to him as a filmmaker. Someone like Wes Anderson is also considered an auteur. One can tell a film is made by him just by looking at it. Anderson tends to write, produce and direct his own films, and he has a certain aesthetic that he likes to employ across all his films. One couldn’t imagine Wes Anderson directing an epic war movie, for example. Although I have to admit it would be kinda fun to think about.
If you’d like to read more about auteur theory, French New Wave or La Nouvelle Vague is a good place to start, because this theory is part of that movement. Hope this helps!