Quite simply historiography is one of two things:

1. The study of development of history as a discipline.
2. The study of the writing of historical accounts.

As to why you should care about it, I'd like to lean on a particular sub-discipline within history, the history of American slavery. I'll talk about this sub-discipline as a case study so as to:

1. Examine the development of the sub-discipline of "history of American slavery."
2. Examine how histories of American slavery have been written.
3. Indicate the importance of thinking "historiographically" as well as historically.

So, there were not any book-length examinations of American slavery until UB Phillips 1918 book American Negro Slavery. Phillips was the first person to "weigh in" on the history of slavery in the states, and he did so by examining primary source materials such as the following: slaveholders' journals/diaries, plantation logs and records regarding the purchase and care of slaves, newspaper accounts related to slave auctions, escapes, etc., various laws and governmental pronouncements regarding the keeping of slaves, and so on. Phillips' historical account of slvaery was notable for two reasons: (a) It was the first, and (b) He claimed that first-hand narrative accounts of slavery (i.e. autobiographies written by slaves or ex-slaves) weren't reliable primary sources because the authors were unduly influenced by their white, Abolitionist editors. Consequently, when writing any historical account of slavery, Phillips argued, the historian should not use any first-hand narrative accounts of slaves.

Phillips accusation regarding the unrealiability of slave sources stuck, and for over fifty years, nary a historical account about slavery was written that used first-hand accounts of slavery written by slaves. In this fifty years, some prominent historical accounts of slavery were written, including Kenneth Stampp's The Peculiar Institution and Stanley Elkins' Slavery: A Problem in American Institutional and Intellectual Life. These accounts did challenge many of Phillips' statements regarding slave life (for example, Phillips insisted that American slavery wasn't profitable and would've dissipated on its own and that there was no need to fight the Civil War; both Stampp and Elkins thought these conclusions were a load of hooey). However, neither Stampp nor Elkins challenged Phillips' assertion that first-hand accounts by ex-slaves were unreliable.

It wasn't until 1972 and John Blassingame's The Slave Community: Plantation Life in the Antebellum South that a historical account featured (indeed, focused on) first-hand narrative accounts of slavery written by slaves and ex-slaves. Blassingame challenged Phillips' assertion regarding the unreliability of slave sources, stating that the assertion was based on somewhat racist assumptions, and that slave sources (such as slave narratives) were crucially important for historians to consider when writing a historical account of slavery. In the Preface to his book, Blassingame writes, "By concentrating solely on the planter [that is, on “white” sources], historians have, in effect, been listening to only one side of a complicated debate." So Blassingame did the opposite; he concentrated on slave narratives in his historical account.

Now the problem with Slave Community was this: in writing this account, Blassingame leaned on then-current theories of psychoanalysis to engage in a sort of literarily-inspired psychoanalytic analysis of individual slaves' narrative accounts, which he then projected onto the whole slave population. That is, he examined a handful of slaves' narrative and he maintained that what was true for these slaves must've been true for all slaves.

The way that Blassingame wrote Slave Community irritated some historians, specifically economic (or cliometric) historians; that is, historians who leaned on numbers when writing their historical accounts. To these historians, Blassingame lacked two of the necessary components of rigorous historical analysis: quantified data and a method for inferring how his isolatable discoveries applied to the larger population of slaves.

Along comes Robert Fogel's and Stanley Engermann's 1974 Time on the Cross: The Economics of American Negro Slavery. This book was immensely popular (a best-seller at the time) and immensely controversial. Though Fogel and Engermann agreed with Blassingame that first-hand accounts of slavery by slaves were important, they maintained that his use of psychoanalytic theories was too wishy-washy. Blassingame didn't have, according to Fogel and Engermann, a good method for analyzing and drawing conclusions from primary sources. So, in Time on the Cross Fogel and Engermann set about counting types of accounts of different aspects of slavery as they were written in these slave narratives. In doing so, they reached some pretty unpalatable conclusions. For example, Fogel and Engermann concluded that whippings/beatings probably weren't as prevalent as people think because the slave and ex-slave authors of narrative accounts didn't mention whippings/beatings all too often. Nevermind the fact that when they did mention whippings/beatings, these narrative authors indicated that they were a common occurrence.

Time on the Cross generated a huge backlash in the historical community. On the one hand it claimed to do all the best things a historical account of slavery could do: it examined white sources and black sources, it had a clearly defined methodology, it had a mechanism for projecting its conclusions onto the whole population of slaves in the US. On the other hand, it challenged things which the world of historians had taken as truth regarding slavery: slavery was brutal, slavery was inhumane, slaves suffered incredibly during bondage.

Time on the Cross even inspired a book-length critical response: Herbert Gutman's Slavery and the Numbers Game, which acknowledged that Fogel and Engermann did good things when composing their historical account (use variety of primary sources, develop a solid method, develop a projection mechanism), they just didn't do a good job at employing these tools when writing their account. That is, they had the right tools, but they didn't use them correctly.

SO WHAT DOES THIS HAVE TO DO WITH HISTORIOGRAPHY?

Today, when writing a historical account of any aspect of slavery, it's important for the historian to know the following things:

1. What accounts of slavery have already been written.
2. How those accounts of slavery have been written insofar as primary source material, methodology, projection mechanism, and so on are concerned.
3. What kind of historical account s/he (the historian writing the new account) wants to write insofar as primary source material, methodology, projection mechanism, and so on are concerned.
4. Where, in the library of historical accounts of slavery, his/her historical account will fit. Will it be like Phillips' account that discredits black sources? Will it be like Blassingame's account that focuses solely on black sources? Will it use a cliometric approach like Fogel and Engermann? Will it use a social scientist approach like Blassingame? Will it challenge previous historical accounts like Stampp's, Elkins' or Gutman's?

TL;DR Historigraphy matters because in order for a historian to write a good account of the past, s/he must be aware of what other good (& bad) accounts of the past have already been written, and how his/her account of the past will align (or challenge) those accounts.

On top of what everybody else has said, where I did my graduate work one of the big questions that kept being reiterated was the "so what?" A huge problem with academic work is that the topic is so obscure that nobody really cares about it, even other researchers. In order to create meaningful work, the researcher has to answer the "so what?" question in a way that other people care about. And "well, nobody ever researched this before" or "it's about x and x is important" aren't good enough answers.

The historiography is one of the ways historians find their so what. By connecting their current topic to what other researchers have said in the past, they help fit their research into the big conversation that everybody is having and give other historians a motivation to read the new research and respond to it. If they can't connect their topic to the historiography, they might as well shove their work into a drawer, because they're not in conversation with anybody.

In one of your responses, I saw that you mentioned history's bias. This is certainly true, to the extent that now when I write my upper-level history papers I'm not allowed to even mention "bias" because it's such a given.

One source of this bias in history is the thoughts and beliefs of the time period during which a "history" was written. As much as I hate citations when I'm writing, I've never been more grateful for them than when I am reading an older history book, that considers itself fact but never cites its sources. You even read histories in the 20th century that have several assumptions, never cited, that they just accept as fact. I personally love local histories written in the 1900's because they throw in bits of unsubstantiated gossip about a person that would definitely not be taken seriously today. Examples from my research are Hull's Annals of Athens and Temple's The First Hundred Years. Here's an example of local gossip that you wouldn't see without some citation today:

"Colonel Cobb was a large man, over six feet in height, weighing not less than three hundred pounds. This portliness which men do not usually attain until somewhat advanced in life, gave him the appearance of being older than he was, and he was called the old Colonel by his elders, which used to vex him no little." (Annals, 61).

If this gossip is accepted as fact in a history as recent as 100 years ago, you can see where we get in deep water as we go back even further. How much of this is subjective? Let’s go back to ~1136, when Geoffrey of Monmouth wrote The History of the Kings of Britain. Sure, it says history, but it also talks about when England was inhabited by giants. It’s now considered pseudohistory and wildly inaccurate, unless you’re tracking the myth of King Arthur, but was believed to some extent to anywhere as late as the 16th century, Wikipedia tells me (sorry). Imagine, how many contemporary histories (historians writing about their day and age) would be using this piece of fiction as a historical source!

Finally, in studying historiography we can trace how religious and gender biases affected “facts” in prior histories. For instance, when the white settlers came to the Americas, they were almost all Christian, and thus had a hard time understanding many of the native customs. Many native societies were matrilineal, and the Cherokee in particular had female chiefs as well, and the white settlers tried to stifle this in their forced conversions into Christianity. In Virginia in the 1700’s, women who refused “proper” roles like marrying or working at home were considered “troublesome,” so you can imagine how they viewed Native American women as trading partners and voices of authority. This is where we begin to see how the white historians write out Native customs, both religious and political. Not many native histories remain, so the only understanding we have of some ancient cultures are what the Europeans/white settlers tell us. And we know that many were unwilling to look past their Christian beliefs and biases. And that’s not even taking into account their opinions of inferiority as something determined by God…

And this brings me to my other women point. I always have a women point. We read of the Founding Fathers, we read of male painters and scientists, and not much in the way of women in history as anything other than as wives or mothers of famous people. Sometimes, this is honestly due to the fact that many women could not read, vote, fight in battles, or govern, and that’s what we consider important when we read old histories. But another reason for this is because the (predominantly male) historians write out women’s accomplishments due to their beliefs that women were literally less intelligent, second-class subservient citizens. Looking back now, with more of a “feminist” lens, historians are able to see female contributions in areas that past historians wrote out. I absolutely love this article about a female artist who is depicting more female artists who were famous in their day, but not written about in the male-dominated canon of art history. As Virginia Woolf famously said “Throughout most of history, Anonymous was a woman.” Here’s an article of female painters during the Italian Renaissance. Ever heard of a single one of them? Me neither.

I didn’t plan on this being a novel and I apologize. Basically, past histories were heavily influenced by beliefs of the day, many lacked citations, and it’s fascinating to study them and see why certain things were left out.

That's a great explanation about historiography. And US slavery is a good topic to examine the development of historiography of a significant time in our past. Interestingly, historian Eric Foner, one of the foremost experts on Reconstruction has a good discussion on historiography in his book Reconstruction: America's Unfinished Revolution and how the understanding and interpretation of reconstruction (and its aftermath) have changed in since he 1860's.