An unlisted video does not appear in the video listing on the homepage of your video website. It is not searchable for those arriving on your video website homepage. However, you can share a link to an unlisted video with a viewer, and they will be able to navigate to your other videos through your video website homepage, and also access search and any other pages on your site.
This setting is useful for making a video available via a link to only the people you share it with, however, it's important to keep in mind that there is no technical mechanism that might prevent someone from sharing that link with other people.
Open the video in question and find the Privacy Settings box. Check the box to "Hide on Video Website" and click "Save" to update the video: