Biblical minimalism is the idea the Bible is not a reliable source of historical information. Minimalists argue that the authors of the Bible were basically the ancient equivalent of novelists, inventing characters and then putting those characters into situations that they also invented. Biblical minimalism can be contrasted with Biblical maximalism, the idea that the Bible can be trusted as a historical source.

The debate about the historicity of Biblical stories is particularly heated with respect to the Hebrew Bible (what Christians call the Old Testament and what Jews call the Tanakh). This is because very few written sources about the Bronze Age survive. If the Bible is accurate, then it is a crucial source of information about the ancient Near East. If it isn't, then our knowledge about several ancient Near Eastern cultures and historical periods simply vanishes.

As a result, the historicity of the Bible is an important issue even for people who do not happen to be Christian or Jewish, since accepting or rejecting the stories in the Bible makes a huge difference in how much we know about life in the ancient world. When the archaeological record is so sparse that we do not even know for sure where entire cities were located, any written source is precious.

(The New Testament, by contrast, describes a time period that is well attested in other sources. Obviously religious people will care about the historical information in the New Testament for other reasons, but it is not quite as critical for understanding details like the location of ancient settlements, the names of ancient rulers, technology levels and government styles. Nevertheless, if you have ever doubted the possibility that a government would require everybody in the country to go back to their distant ancestors' hometowns to be counted for a census, then you've felt the stirrings of Biblical minimalism.)

In any case, what minimalists and maximalists argue about is "background" information: they don't care much about the philosophy or ethics of the Bible for the purpose of this particular debate, but they care very much about whether, for example, the people who lived at the time of Job would have lived in houses or tents. (I'll get into my reasons for mentioning this in a minute.) Not surprisingly, many minimalists are agnostics or atheists, while most maximalists are religious -- but the correspondence is not total in either direction.

Reasons why someone might come to a minimalist position include the following:

1. Mythical material. The first element of Biblical stories that arouses doubt in many readers is usually the "miraculous" stuff: putting all the animals in the world on one boat, making a path through the sea and having it close up behind you, stopping the sun in the sky long enough to finish a battle, and so on. Even religious people are often unwilling to commit to the historicity of these stories, choosing instead to read them as metaphorical or symbolic. Holding that position does not in and of itself make someone a minimalist, since at least in theory someone who rejects supernatural elements of stories may still accept the historical claims of those same stories. Nevertheless, for many readers the mythical material in the Bible casts doubt on the rest of the Bible as well. The stories in the book of Genesis, particularly the creation and flood myths, were important factors in the development of minimalism as a position within Biblical studies.
2. Technological anachronisms. A modern reader, enjoying a novel set during World War I, would probably do a double-take if she were to find a scene in which a soldier flips open a laptop. If a historian tries to write a non-fiction account of the First World War and has soldiers chatting in Skype, he would probably lose his job and the book would never get published. One of the riddles of Biblical analysis is to figure out whether the technologies and governments described in the books match the times in which the stories are set. To choose a simple example, Job 1:13 describes a house collapsing and killing a family, but if living arrangements in ancient Uz did not include walls -- if, for example, Job's compatriots would only have known tents -- then that suggests the story was written many centuries later than the events it describes. If the author of Job was clueless about the difference between houses and tents, how much can we trust him with the other details of the story?
3. Political anachronisms. Imagine reading a story in which George Washington is described as a member of the Republican Party. Whether Washington would have sympathized with the modern Republicans is up for debate, but the fact of the matter is that he could not have been a member since the party as an institution was not created until half a century after his death. Similarly, it is important to know when cities were founded and what they were called at various times in their history (was your story set in Leningrad or St. Petersburg?), the birth and death dates of rulers, the names and zones of influence of various organizations, and so on. Figuring all this out is very delicate and difficult work, especially since there are very few comparanda for Biblical sources. (In other words, if we reject the Biblical version of events, there's often no fallback plan: the state of knowledge is reduced to zero.)
4. Internal contradictions. If you believe that a single contradiction in a story casts the entire thing into doubt, then you'll probably adopt some flavour of Biblical minimalism. The author of the book of Samuel can't decide whether Michal had no children or five, which means that he may well be wrong about other details of Michal's life. Hardcore minimalists take this to mean that Michal was a completely legendary figure, along with everybody else in the Hebrew Bible -- some of them go so far as to doubt the real-world existence of important characters like Moses. The authors of Kings and Chronicles can't even agree on how many stalls King Solomon had for his horses, or how many years of famine King David bargained with God for -- this raises a lot of questions about their trustworthiness on other matters.
5. Contradictions with other sources. In many cases -- too many -- the Biblical account is the only surviving record of an era. However, sometimes it's not. In these cases, the Bible often fares poorly when compared with other sources. For instance, according to the Biblical account, the Israelites were such an annoyance to the Egyptians that the Egyptian government went to bizarre lengths to wipe them out. However, the ancient Egyptians kept excellent records for thousands of years, and never mention these supposedly numerous and troubling Hebrew slaves. Biblical apologists will say that the Egyptians have plenty of political reasons to pretend that the Exodus never happened, since the escape of thousands of slaves under the banner of a lisping Hebrew leader is quite an embarrassment to them. But there are other ways to weigh this evidence beyond just "he said, she said". For instance, a minimalist might argue that the numbers in the Biblical account aren't realistic -- that the 600,000 Israelite men of Exodus 12 (just men!) couldn't have stomped through the wilderness for forty minutes, much less forty years, without being remarked upon by every literate tribe in the known world.
6. Physical evidence. For minimalists, archaeological findings always trump written sources. The assumption is that human beings have myriad reasons to lie while objects simply cannot. Therefore, a minimalist will always trust city ruins, pottery shards, and bones over the written words of men and women with political agendas. It is probably no surprise to you that the physical evidence for a worldwide flood is nonexistent; however, the physical evidence for "social" Biblical phenomena is also doubtful. For example, the book of Joshua describes a war in which the Israelites conquered the land of Canaan. Wars leave traces, and archaeologists are pretty good at finding the remains of slaughtered populations and torched villages. The evidence for an invasion in Canaan of the sort that Joshua describes cannot be placed anywhere in the thirteenth century BCE, when it was supposed to have happened, and some archaeologists say that evidence can't be found in any century at all. Similarly, the vast riches imagined to belong to Israelite kings like David and Solomon have not been unearthed even after centuries of searching. It doesn't mean they never will be, of course, but the sorts of palaces and stables described in the books of Kings and Chronicles usually can't stay hidden for long.

There are several shades of Biblical minimalism, ranging from "we need to be skeptical about certain historical claims in the Bible" all the way down to "the whole thing was made up out of whole cloth." The latter, more radical view -- associated with the Copenhagen school of archaeologists -- can be startling even to atheists, who usually grant that Jesus or King David or Hezekiah were based on real people, and that other Biblical stories carry at least a faint memory of real events. Radical minimalism is troubling even to those who have no interest in or commitment to the Biblical God, because it suggests that writers can go through inordinate amounts of effort to write histories of places and events that never existed -- complete with genealogies, census data, and inventories of goods. Novelists do that from time to time, of course, but few novelists expect entire cultures to base their morality on the exploits of a nonexistent king whose nonexistent lineage is traced over twenty pages. It is easier, in other words, to imagine some earnest exaggeration about real events than it is to imagine a massive Bronze Age social experiment created ex nihilo.

To some extent, arguments about Biblical minimalism and Biblical maximalism will always be circular. People who trust the Bible trust it "because it says so" or "because it's there." People who don't trust it often have very little to compare it against: in too many cases, there is no other source to "prefer", or the preferred sources are difficult to interpret. (Shards of pottery don't lie, granted, but they also don't tell us much about politics or law.) Thus the radical minimalist has to have an extremely cynical view of human nature, one that says that people really will create a religion out of something they just made up, and, more strangely, that people will actually sign up for that religion. Furthermore, fresh stories rarely include as many awkward details as the Bible seems to admit (the Israelites' background as slaves, the strange crimes in Moses' past, the multiple failures to wipe out indigenous Canaanite religion), which suggests that whatever reality the Biblical authors were writing about was pushing back -- at least a little bit.