What difference does it make if I enable support for video post format?

Couple of things to point out actually:

1. It will add a class on post_class() so you can use different formatting via css.
2. In the case of Post Formats, the taxonomy is post_format and the terms are post-format-{format}. i.e. taxonomy-post_format-post-format-link.php http://codex.wordpress.org/Template_Hierarchy
3. In single.php file you can use conditionals to have complete different html for each post format.
4. Hopefully there are more but can remember right now 😉