Hiding a Categories content on just the Homepage ‘Posts’?

Okay, it sounds like you’ll want to modify the primary Loop using query_posts(), but only on the Site Front Page.

I don’t think TwentyTen includes a front-page.php template file, so we’ll modify index.php directly. Add the following code to index.php, anywhere before the Loop output:

<?php
// Determine if we're on the site Front Page
if ( is_front_page() ) {
    // Globalize $wp_query
    global $wp_query;
    // Create argument array in which we 
    // exclude desired category IDs. Categories
    // are listed as a comma-separated string.
    // e.g. '-3', or '-1,-2,-3'
    $exclude_cats = array( 'cat' => '-3' );
    // Merge custom arguments with default query args array
    $custom_query_args = array_merge( $wp_query->query, $exclude_cats );
    // Query posts using our modified argument array
    query_posts( $custom_query_args );
} // is_front_page()
?>