I created a video album but I would like to display that album only my my video link on my website. Is there a way to exclude album title and description for one particular album from showing up on the main theme index.php page? For example, I would like to exclude the video album from displaying its thumbnail, decription and link in my main gallery so I can just point to it manually on my video page.

You can mark the album unpublished. Then it it will not show up (except to logged in admins.) But you can still link directly to it and then view it with a manual link.