An archive usually means a backup of certain content.
In some cases it is also used in expectation of mods deleting a thread, to provide evidence of what was once there after it is removed.
Paranoia sometimes happens when archive.org fails to display a thread. Especially since there is sometimes a record that there was an archive made of it.
As can be demonstrated through experimentation though, there is a delay on an intermediate 'save' page where archive.org compiles content from the page.
If a user closes the tab before that process finishes it can result in an incomplete entry, where archive.org will do the first step of creating the date/time link for that URL but not actually complete the second step of logging the data where that link directs to.
This can result in conspiracies that FBI or other secret organizations controlling archive.org have scrubbed the page which may not be accurate, as it could simply be due to negligence of the archive submitter.
Such negligence could be accidental (they're in a rush, they don't know to leave it open, their browser crashed) or intentional (they want to create a failed archive to make it look like they're being censored).
This doesn't mean that archive.org doesn't intervene to take down archives: they most certain DO when it's reported to them, and they certainly could have secret relationships or conflicts of interest. In some cases they pre-intervene by preventing archival of entire websites (or sections of websites) either at the behest of owners or of people who make complaints about the content.
This mix of possible explanations can lead to a lot of uncertainty and guesswork about the fates of certain archives. The best way to know is for multiple parties to submit their own archives and make sure the process is complete.
It is also possible to submit archive.org archives to archive.is and make copies there, even if the original content is no longer up.