Enable "allow_url_fopen" and "allow_url_include" in "php.ini" file to let Youtube Gallery request thumbnails, titles, descriptions, playlists etc.
If you have shared hosting you may create a file named "php.ini" with lines below and upload it to site root and administrator folders.
Refresh Video Lists and clear Joomla cache.
Tip: It may help if you increase timeouts:
max_execution_time = 120 ; Maximum execution time of each script, in seconds
max_input_time = 120 ; Maximum amount of time each script may spend parsing request data
Install cURL more info here.
Install DOM library, if it is missing.
You may delete these php.ini files when all videos and it's titles are fetched.