On computer file systems, different files and directories have permissions that specify who and what can read, write, modify and access them. This is important because if the app does not have permissions to read and write certain directories some functionality will not work.
In most cases you will not need to change permissions manually, unless you are experiencing file permission related errors.
Permissions will be different from host to host, so this guide only details general principles. It cannot cover all cases. This guide applies to servers running a standard setup.
If you are seeing an error like The stream or file "/some/file.php" could not be opened: failed to open stream: permission denied, you will need to change file permissions on your server via file manager. Most hosting providers will have one built-in into their control panel or you can use an FTP client like FileZilla for windows or Transmit for mac.
Usually you will need to change permissions for folders to 0775 and permissions for files to 0644.
In most cases you would only need to change permissions for storage folder.
If permission error is for a specific file, you will most likely need to change permissions for the parent directory of that file.