This is a little confusing, so be gentle with us, because we are confused, too.
Let's cut out the introduction and look at the rest of the book for a moment. Oh, that's much easier because the narrator for most of the book is someone who isn't in the story and who can freely dip into many different characters' minds.
Most of the book comes from Abraham Lincoln's journals, so we get to hear a lot about what he thinks of things. (Which is pretty ordinary if you've ever stolen a look at someone else's journal or blog.) We hear about Abe's thoughts and feelings all the time.
When Abe is in NYC, he discovers that three men (ahem, vampires) are following him and Abe writes in his journal, "How had they escaped my notice until now? In light of the city's recent troubles, I thought it best to double back and head south to Washington Square, back to the safety of gaslight and crowded streets" (9.67). That example was chosen at random, just as proof that every chapter has some moment when the narrator gives us Abe's thoughts.
But every once in a while, the narrator will give us some other character's thoughts. For instance, when Abe asks Henry why Henry uses Abe to hunt vampires, we get a glimpse of Henry's feelings: "Henry ran a hand over his face. This was a conversation he had hoped to avoid" (6.154). So there we get to know something internal to Henry—something that we would only know if we were looking at the world from Henry's perspective.
And this dipping into others' consciousnesses doesn't just happen with a few, major characters. It happens with the little guys, too. When Willie is poisoned by a vampire, that vampire runs away while being chased by Abe's vampire bodyguards, and we get this: "The river... I can lose them in the river…" (11.78). Now, this is a minor character, a vampire who doesn't even have a name and will soon kill himself. And yet, the narrator can even look into this character's mind and tell us what that character is thinking.
This is a classic omniscient (all-knowing) third person narrator; and this sort of narrator comes in handy for a tricky story like this one. That is, this omniscient narrator can flash forward or flash back to give us the big picture of history or the biographies of the historical characters. We get a healthy dose of perspective every once in a while that there's a larger story going on that we should be keeping in mind.
For example, the narrator tells us that John Todd Stuart "would play a crucial role in Lincoln's postwar life, as an encouraging lawyer in Springfield, as a friendly adversary in Congress, and most of all as the cousin of a raven-haired Kentucky belle named Mary Todd" (6.32). Helpful, right? That makes this book a lot easier to read, because you could easily get lost with so many characters drifting in and out. And so many characters named John.
The introduction is told in the first person by a character named "Seth Grahame-Smith" who isn't very important to the story. In fact, he's so unimportant that the story doesn't even return to tell us about him after Abe's story ends. We meet him once, and then he splits. Sort of.
Apparently, good ol' Henry Sturges has tasked Seth Grahame-Smith with writing a manuscript of Honest Abe's journals, so that the truth might finally be told about everyone's favorite president. On the one hand, it's really useful to have an ordinary guy from our time filter the info from Abe's journals. He can explain stuff to us and clean up Abe's terrible spelling.
On the other hand, how does Seth-Grahame-Smith-the-narrator know all the stuff that's in this book? Sure, he has the Lincoln journals; and he does have a list of names for people to interview (Introduction.74). But how does he know some of the thoughts that he puts in this book?
For example, the vampire assassin who kills Willie and then kills himself—he's not around for an interview, right? But still Seth-Grahame-Smith-the-narrator gives us a little view of his thoughts (as we said above). So how does Random Modern Guy know all these thoughts and ideas from ye olden times?
(1) Seth mostly tells the truth. Most of the book faithfully tells Lincoln's thoughts (from the journals) and adds some extra info that Seth got from interviewing people and vampires who always tell the truth. The only info that Seth adds/makes up are little details that are reasonable to assume. If you read it this way, then the narrator is mostly important as a way to make it easier for us to understand history and we can totally trust his version.
(2) Seth can't entirely be trusted. Maybe Seth isn't a liar, but who knows if his vampire interviewees are telling the truth? (After all, think of all the info they leave out, like, where is Abe Lincoln now?) If you read the book this way, then "Seth" tells us a version of history that we can't really believe in 100%.
And that makes some sense in this book since it is forever reminding us that history isn't what we think it is. Abe fights slavery? That's what we learn in history class, but the true history is about vampires. Perfect, then, that Seth tells us a version of history that looks like it's omniscient ("this is what really happened") but can't really be totally omniscient.
History is messy, folks. And those who tell it aren't always what they seem.