Agnes gets the first and the last words of the novel, so even though she’s only alive for about five minutes at the beginning, we figure she’s actually pretty important.
Agnes, we later learn, is nineteen years old when her father’s new friend (who is about thirty or so) falls in love with her. She is young and has never been in love before, and she falls for him. He keeps saying that he can’t get married, but is mysterious as to the reason why. Eventually, they have sex and she gets pregnant (major whoopsie). Her lover is called away to Italy, and dies there, and she runs away from home to avoid shaming her father by having a child out of wedlock. And that’s where the story picks up in the first chapter: she arrives at a workhouse, has her baby, and dies.
Fine—the book is about an orphan, so it makes sense for it to open with a baby being born and a mother dying. But the book’s supposed to be about Oliver Twist, though, and not his mother. So why does she get the last lines, too? The last passage of the novel describes the memorial tablet Oliver and Rose hang in the church for Agnes, and the narrator says,
I do believe that the shade of that poor girl often hovers about that solemn nook—ay, though it is a church, and she was weak and erring. (53.16)
Okay, so Agnes was "weak and erring." So she had sex before marriage. The narrator and the characters keep harping on that, but they seem perfectly willing to excuse the same fault in Oliver’s father. And he should have known better! He was older, and had already had one son, so presumably he knew how the whole baby-making thing worked.
So, for a novel about "crime" in general (fraud, theft, murder, prostitution, etc.), it seems important that the novel both open and close with a reference to another "crime"—having sex (and children) out of wedlock. And that wasn’t actually a crime, legally, but it sure was a crime socially. By book-ending the novel with Agnes’s shenanigans, is Dickens trying to present crimes against Victorian social mores as somehow equal to crimes like theft or fraud?