Abe doesn't cut the heads off vampires with his journals, but they're still important to his vampire-hunting career and his personal growth.
Purely on the non-vampire side of things, we can see how Abe grows up and learns through his spelling. Yes, this is a book about Abe Lincoln hunting vampires and we're talking about spelling.
When Abe first starts his journal, his writing is full of errors, both spelling-wise and grammar-wise, which the narrator nicely points out by using "sic." (You use "sic" when you're quoting something that has an error and you don't want people to think that you're the one who messed up. It basically means "can you believe this fool?")
For example, take a look at this quote: "Henceforth my life shall be one of rigerous [sic] study and devotion. I shall become learned in all things. I shall become a greater warrior then [sic] Alexander" (2.93). So Abe misspells "rigorous" and uses the wrong type of "than"; this is a kid who needs to study more.
Which he does. By the end of his life and journaling, Abe Lincoln has learned a lot more (thanks to people like William Mentor Graham); and his writing is more correct. We also can tell that these journals chart how Abe grows up and learns because the narrator tells us that: when "Seth Grahame-Smith" first looks through the journals, he notes, "As I read them, I saw the author's penmanship evolve from the overcautious script of a child to the tightly packed scribbling of a young man" (Introduction.7). Ah, the wonders of coming-of-age through penmanship.
This may be shocking but growing up doesn't mean you're always right. The Lincoln Journals may chart Abe's process of growing up, and he certainly does learn more, but sometimes Abe doesn't really know what's true. Sometimes his version is just plain wrong.
That means that the narrator has to step in on occasion to make corrections. This happens at the beginning of Abe's career, when he uses the word "kill" when he's talking about vampires and the narrator adds a footnote saying that "kill" isn't really the right word to use with vampires since they're already dead (2.93).
But this also happens towards the end of Abe's career, too. For instance, when Abe wins the presidential election, he writes, "I admit it came as little surprise, for I believed that the Union would see to my victory—whether earned or not." And then we get the footnote correcting Abe: "There was no cause for the Union to intervene—Abe comfortably won the election on his own merits" (10.158). Even when Abe's older, apparently, he can still be a bit off base.
But his journals aren't just about how Abe is wrong; if he were always wrong, these journals wouldn't be useful at all. Sometimes, the issue isn't "Abe thinks X, but really it's Y." Sometimes the important issue is simply that Abe thinks or feels X—and he feels it very strongly.
Thanks to Abe's journals, we get to hear all about his feelings and what he thinks about, like Ann Rutledge, his first love: "She is the most fetching... most tender... most brilliant star in the heavens!" (6.73). When we read that, we get a sense of Abe not just as president, but as a regular(ish) person having regular(ish) feelings, albeit a bit more poetically.
Abe doesn't just use his journal to record his obsessive love thoughts; he uses his journal to record his thoughts about death and loss, too. When he loses to Stephen A. Douglas, Abe gets depressed and notes, "I have failed the oppressed... the helpless faces crying out for justice. I have failed to meet the expectations of freedom-loving people everywhere" (10.21).
We might look at that and say, "Abe, get a grip. It's just one election." But whatever we think about this, the journals help us see what Abe thinks about this, and that's really what we're interested in, right?. And so the journals give us the inner world of Abe, who isn't an unfeeling portrait of a president—he's a regular(ish) person who feels pretty strongly about things.
So the journals show us that Abe (1) grows up, (2), isn't always right, and (3) feels strongly about things. In other words, we could say that the journals symbolize how human Abe is.