Categories

yes

If you are not a coder, check out this plugin
http://wordpress.org/extend/plugins/advanced-category-excluder/

If you do code, check out
http://codex.wordpress.org/Template_Tags/query_posts
You are interested in the Category Exclude option
Basically you would add a one line query_posts() before the loop, in index.php, to exclude the category you don’t want on the homepage.