The last words of “Bartleby the Scrivener” can be seen as a lament for the sheer absurdity of Bartleby's existence. They come after the lawyer narrator, Bartleby's former employer, has heard a rumor that the troubled young man once worked at the dead letter section of the post office.
Dead letters are those belonging to people who are now dead, and, as they cannot be delivered, need to be destroyed in order to protect their contents. The lawyer seems to think that the piles and piles of dead letters, and the absurdity that they represent—after all, letters that cannot be delivered are absurd—somehow must have unhinged Bartleby, leading to his odd behavior.
The final words of the story can also be seen as an expression of exasperation on the lawyer's part at the absurdity of life as a whole, not just Bartleby's life. That's why the lawyer exclaims “Ah, Humanity!” He clearly thinks there's something absurd about human existence, and this makes him a kind of proto-existentialist.
Little wonder, then, that Melville was such a favorite of Albert Camus, the famous French existentialist writer of the 20th century. In the figure of Bartleby, he clearly saw the prototype for the existentialist heroes of his own fiction, struggling vainly to survive in a world that is fundamentally absurd.