In addition, he preserves material that's missing from the Bible, like the connection between Cain and materialism, the reason the Tower of Babel was constructed of pitch, and details about such New Testament figures as John the Baptist and Jesus.
But with his massive trove of information and analysis also comes vexing uncertainty: We don't for sure what he wrote, and we do know for sure that along with reporting history he made things up.
We know because Josephus himself tells us so.
The sheer volume of material that Josephus left is impressive. His Jewish Antiquities alone runs to half a million words in English translation. Equally remarkable is his attention to detail and the breadth of his knowledge.
Unfortunately, three concerns potentially diminish Josephus's value. He writes about things he could not possibly have known (like conversations at private meetings during which no minutes were kept). He errs considerably regarding some objective facts. (He puts the height of Mt. Tabor at more than 18,000 feet, when it actually only rises 2,000 feet.) And his original writings survive only in obviously inaccurate copies and translations.
On the positive side, the copies and translations are not completely wrong (with the probable exception of his "Testimonium Flavianum" about Jesus), many of his facts are independently verifiable, and it was common in antiquity to invent dialog to support historical narrative.
So on balance, Josephus is an invaluable source for understanding the Bible. And a fascinating one.
For instance, reporting on Genesis, Josephus charges biblical Cain with materialism, writing that "Cain was not only very wicked in other respects, but was wholly intent on acquiring things." The Hebrew word for "Cain" (kayin) shares the root k.y.n with the Hebrew verb for "acquire" (declined as kaniti in Genesis). And it's common in Genesis for a name to signify some quality of its bearer. So Cain's materialism doesn't seem to be something that Josephus invented. Rather, he appears to be reporting a tradition that was somehow omitted from our text of the Bible.
Similarly, Josephus explains that the purpose of the Tower of Babel was to defend against any future flood. The people built it so they wouldn't be subject to God's destruction and could therefore do whatever they wanted. This is why the tower was waterproofed with bitumen. Though the Bible agrees that the Tower was constructed with bitumen, the text there doesn't give any rationale. Only Josephus does.
Bitumen appears in two other places in the Bible: Noah's ark and the basket in which baby Moses floats down the Nile. Both of these would require waterproofing. So it appears that Josephus was again preserving an ancient tradition when he connected the Tower of Babel to the Flood — a connection that was left out of the official text of the Bible.
For instance, it is primarily Josephus who helps us sort out the significance of the various people named Herod, indirectly explaining why it is so hard to appreciate the impact of the Gospels without knowing who Herod the Great was.
Josephus also helps readers make sense of the animosity between the nascent Church and the Roman rulers of the day, such as when Paul mocks the king.
In Acts 25, the local governor Festus tells King Agrippa about Paul, who has been imprisoned because of "certain points of disagreement" between Paul and the Jews about "their own religion." King Agrippa agrees to investigate the matter for himself, which is how (Acts 25:23) Paul appears before "Agrippa and Bernice."
Having been granted this royal audience, Paul recounts his good fortune that it is Agrippa who will adjudicate his case, because, Paul says to the king, "you are especially familiar with all of the customs and controversies of the Jews." Though Paul is only addressing King Agrippa, Agrippa arrived with Bernice. The obvious presumption is that Bernice is Agrippa's wife.
But we read in Josephus that she is his sister, with whom he is engaged in an incestuous affair! Armed with this knowledge, the reader recognizes that Paul is mocking the king, and that the trial is a farce. Without Josephus, we might have no way to understand Acts 25 properly.
The first and more important one comes as Josephus portrays the ongoing battle between the Romans and the Jews. To demonstrate the nature of the conflict, Josephus describes how a High Priest named Ananus summons a man before what appears to be an arbitrary council. The man whom Ananus summons is "the brother of Jesus whom they call Christ,1 whose name was James."
Ananus's role here is merely as a demonstration of the political strife, so the details of who appears before him are entirely unimportant, except that one such man just happens to have a really pivotal brother: Jesus. Because Josephus isn't even addressing Christianity here, this is striking confirmation that Jesus was important and well-known enough that even a cameo by his brother was newsworthy. (On the other hand, the fact that Jesus had a blood brother is a theological problem for some.)
The second passage is more famous and has earned its own title: "Testimonium Flavianum," that is, the "witness of Flavius" Josephus to Jesus's divinity. In it, Josephus describes Jesus as "the Christ," wondering "if it's proper to call him a man, for he was a doer of wonderful works." Unfortunately, we have no reason to think that Josephus actually wrote that passage. Rather, it seems to be a later insertion.
Still, even without the Testimonium, Josephus preserves traditions that were cut from the Old Testament and fills in blanks in the New Testament — all in addition to his remarkable contributions to history.