No, not Leon: we just mean he looks dang good in a suit. Actually, Joseph Gordon Levitt showed up for his audition wearing a suit and unintentionally matching his character's get up...perfectly.
Arthur is the professional member of the team; he's the glue that holds it all together. Everyone is important but with the wavering mental state of leader-in-chief Cobb, the newbie Ariadne, jokester Eames, tourist Saito, and Yusuf (who can't drive), it falls to Arthur to really run the operation.
He's in charge of a lot of the planning process we see during that montage scene where everything starts to come together. It's no fun to be called a stick in the mud, but someone needs to take charge.
There's no questioning Arthur's professionalism (except for kissing Ariadne. Come on Arthur, that's a sexual harassment lawsuit waiting to happen), but we can't help pointing out that everything he's doing is completely illegal.
We know Cobb's story, about how he's forced to do illegal work because he's accused of a crime he didn't commit (well, sort of didn't commit), but what is up with Arthur? He seems like such a sensible person but he isn't opposed to setting up shop in some random Paris warehouse to hack into a powerful energy mogul's mind and plant an idea in it.
That doesn't make him sound levelheaded—that makes him sound like something between a thrill-seeking, unscrupulous daredevil and just plain… crazy. In fact, he's the guy who tells us inception isn't even possible, so why does he go along with it all?
Uh, we can't answer that question.
If we had to guess, we might compare Arthur to Ariadne who's drawn to the mystical world of dreams. Then again, maybe he's just good friends with Cobb and wants to help him out, or maybe he likes money. We're guessing being an extractor pays pretty well.
Our Personal Dream Portal
Without Arthur, the audience would be more than a little lost. Nolan is doing some pretty crazy things with this movie, and, as the audience, we're stuck trying to make sense of it all.
Luckily, Cobb and Arthur tag team the explanation process (mostly to Ariadne) so that we can all understand exactly what's happening. Arthur walks us through the difficulties of inception, the importance of paradoxes and some other key things like the initial military development of dream sharing (hmm, makes you wonder how much Christopher Nolan really knows) and how kicks work.
That leaves us with a question:
What does Arthur do… like actually do?
Sure he is well dressed and helps explain things to the audience; he has a role in the film and a role in the plot of the film, but what of his role in the actual extraction? Eames says that he's "the best" at what he does, but we never find out what that is.