Two things: characterization and language.
His characters are remarkably complex, even when compared to those in novels which revel in self-analysis. And he found ways to evoke sympathy for all kinds of characters, even those who are unabashedly bad.
His use of language is unparallelled. He uses a huge vocabulary and a rich wealth of literary technique, but what he is most remarkable for is being able to say very important and deep things in a very compact way. A sentence of Shakespeare tells you more than pages of other writers. And he does it in iambic pentameter to boot.