To add a bit to what others have said, as a writer, I think he has some of the best dialogue I’ve ever seen. Of course, even the best dialogue needs to be well performed, so obviously that also points to his ability to choose the right people to play the roles and give them good direction. That he can build so much tension with just dialogue is amazing.
For example, the opening scene in Inglorious Basterds, with the Colonel talking to the farmer, it’s a very tense scene largely carried by what, on it’s surface, seems like fairly mundane chatter, it has a hint of humor to it, and you really get all the character development you need for the villain, and it sets the tone for the whole film. The movie as a whole has some issues, but I think that’s a brilliant scene.
He can also do other remarkable things with dialogue besides just build tension. Recall the scene in Pulp Fiction where Christopher Walken rambles about hiding a watch in his ass. In the hands of virtually anyone else, there’s no way that scene could have worked and be taken seriously, but he manages to take such a ridiculous premise and make the audience believe it.
He also has an ability to create remarkably complex characters that defy the typical archetypes that we expect in a film. There’s no real “good” or “bad” people in his universe, instead we have protaganists, some for whom we’re led to sympathize with and some we’re not. Look at Kill Bill, the Bride is hardly a good person and she knows it; hell, she’s out to kill people for doing exactly what she did. And we find out that Bill, despite being a horrible person too, ultimately does have a good side to him, in caring for his daughter and, presumably how he felt for her before he had his…urm… jealous streak.
And, of course, he has his signature style. As someone else pointed out, ultimately, he’s sort of doing a film study and doing an homage to various styles of film. Some directors have more distinctive styles than others, but I think Tarantino’s films are among the most distinctive, and what’s more, is that it fits in well with his skill sets and the themes he’s exploring, whereas some styles are more just distinguished by things that don’t particularly add or detract from those ideas (eg, JJ Abrams and lens flare).