So, all the reporting I've seen is that president Joe Biden “willfully retained” and disclosed classified documents while out of office, but concluded that “no criminal charges are warranted.”

How are those two things not directly contradictory? Isn't willfully retaining and disclosing classified information a crime?

TL;DR - the special prosecutor reported that there was evidence that Biden did these things, but that there wasn't enough to successfully support a prosecution.

Longer version - as we discussed ad nauseum in the Trump classified docs case (and in comparing it to Clinton's email situation), one of the elements of most crimes is a specific mental state on the part of the defendant. This is called mens rea. Many crimes require only "general intent" - they had to intend to do the act, and don't have to have any other particular knowledge or intent. Most crimes involving classified information require "specific intent," which requires some level of knowledge or "willfulness" in order for the crime to have occurred.

In a nutshell, for you to be guilty of willfully retaining classified documents, you have to have intentionally and knowingly retained those documents. Prosecutors have to be able to prove beyond a reasonable doubt that the defendant knew the documents were there, that he knew what was in those documents, that he knew the contents were classified, and that he knew that he had an obligation to return them to the government.

That's typically hard to do - especially in situations where someone (like Biden or Trump) has reams of documents from their time in office and it's hard to prove that they had specific knowledge of the contents of all their file boxes. Trump's in trouble because there's a lot of evidence to support claims that he actually knew that he was in possession of classified documents (namely, the Archives told him that he was and he had his lawyers on his behalf review the documents in response to those claims). So prosecutors can feel pretty confident that they have a prima facie case that the mens rea element was met and can be proven in court.

For Biden, though, prosecutors would have a really hard time proving up Biden's mental state. The special counsel chose a very cutting way of expressing that. Instead of pointing out that it's very likely that someone wouldn't remember the specific contents in dozens of boxes containing thousands of pages of documents (correctly, since that would be true of anyone), he instead pointed out (also correctly) that Biden could offer some specific evidence that his memory is terrible generally.

Anyway, that's why there's no prosecution - because there's insufficient evidence that a crime took place.