Sometimes a YouTube URL can get malformed by adding an extra character to the end or missing a character. It is always smart to copy the URL you are using for Video Background Pro, and paste it into an incognito browser window. If the video does not play, there is an issue with the URL.
The YouTube video that you want as a video background must be publicly accessible. This means that the video must be either public or unlisted, but can NOT be private. You can make sure your YouTube video is publicly accessible by visiting your YouTube video URL in an incognito window to see if it plays.
If you have checked the previous recommendations and they were not the cause of the issue, you may be experiencing an YouTube plugin conflict. This means that you have another plugin installed that is using the YouTube API that is conflicting with Video Background Pro. It is best to deactivate any YouTube plugins one by one on your WordPress site to rule out which plugin is causing the conflict.