This is actually very simple. All you have to do is modify some PHP code.
First, goto Manage > Categories and get the ID of the Category you wish to exclude. Then, go to WP admin and selet Presentation > Theme Editor ..
For your current theme, edit the loop where the posts are displayed.
Here is the sample from K2 Theme’s post display loop.
<?php /* Start the loop */ while ( have_posts() )
{
the_post();
?>
MODIFIED CODE :
<?php /* Start the loop */ while ( have_posts() )
{
the_post();
if (is_home()) if (in_category('14')) continue;
if (is_home()) if (in_category('47')) continue;
?>
The modified code doesnt show posts that belong to Categories 14 and 47 in homepage.