When you click on History, Show All History, then on the little star it shows back up and restore. What is that backing up and what do the dates that are listed represent?
I'm looking to determine if 'back up' and 'restore' are for sessions or for individual browsing history.
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What is that backing up and what do the dates that are listed represent?
That Backing up and Dates listed are Backup Information of the Firefox's History and Bookmarks data arranged Date-wise. If you didn't took the Backup then somebody else who uses your system took the Backup.
This is to back up your bookmarks, which include your history entries also. The dates represent the restore copies of files that are available, and have been created automatically as backups; Do NOT use them unnecessarily.
You should first of all make a manual backup, before considering using any restore because the restore will overwrite existing bookmarks and history.
See
You can also create an HTML backup of your bookmarks. Such an HTML file can also be opened in a browser tab via File > Open File if you need to inspect it or only need to get a specific bookmark.
Importing an HTML backup merges bookmarks with the existing bookmarks, but restoring a JSON backup will always replace all current bookmarks, so you lose those.