A Judaean garrison on an island in the Nile left behind its contracts, its lawsuits and its letters. It is the only substantial body of everyday documents from Judaeans of the fifth century BCE, and almost none of it agrees with what a reader of Ezra would expect.
What they are
Elephantine is an island at the first cataract of the Nile. A Judaean military colony was stationed there under Persian administration in the fifth century BCE, and a large body of its Aramaic paperwork survives: marriage contracts, property transfers, loans, receipts, legal complaints, and letters to and from the authorities.
This is documentary material, not literature. Nobody wrote it to persuade anybody of anything, which is precisely what makes it valuable.
A temple that should not exist
The colony had its own temple, at which sacrifice was offered. That is difficult to square with the centralising programme of Deuteronomy, and the community evidently saw no difficulty: when the temple was destroyed, they wrote to the authorities in Jerusalem asking for support in rebuilding it, and when Jerusalem did not reply, they wrote to Samaria as well.
The letters are dated, name a high priest of Jerusalem, and name the governors of Judah and Samaria. They are among the very few documents that put those offices into a single contemporary frame.
Practice that does not match the prescriptions
Marriage documents record Judaean men married to Egyptian women, with no sign that this was contested locally. Oaths invoke deities other than the God of Israel alongside him. Names in the community combine Yahwistic elements with others.
None of this is scandal, and it should not be reported as such. It is evidence that Judaean practice in the fifth century was more various than the prescriptive texts of the period imply — which is what one would expect, since prescriptive texts prescribe against something.
The distinction that matters
The papyri corroborate a setting. Persian administration, a dispersed Judaean population in contact with Jerusalem, live disputes about intermarriage and about how a temple community should behave — all of that is the world Ezra, Nehemiah and Malachi assume, and it is now attested from outside.
They do not confirm any biblical passage, and no honest use of them claims otherwise. They mention no biblical event and quote no biblical text. What they do is make the period concrete, and give a control against which the biblical picture of it can be read as one account among several.