How to get latest post excerpt from a specific category?

Try this:

$paged = (get_query_var('paged')) ? get_query_var('paged') : 1;
$wp_query = new WP_Query("category_name=$catName&paged=$paged&posts_per_page=1");

Basically, add the paged variable to the args — since it’s your home page, you could hard code it to equal 1, of course.