jugigi what are you trying to do?
Usually you don't need to touch them.
If you're trying to remove the public folder but have issues, it will be easier to download the Flarum archive with the public folder already removed and skip Composer for the initial installation.
The paths are made customizable to allow for the public and non-public configurations, and also allow putting the storage folder in a completely different place on the filesystem if you wanted to. They just point to the path of the folders which are already included in the download, base is the one containing the flarum executable and Composer root. public is the one containing index.php and assets (which will be the same as base if you don't use a separate public folder). storage is the storage folder. site.php should be left in the base folder and included as a relative path from index.php and flarum.
