excerpt not showing up

Inside a template file, the standard loop syntax will display only the information about that page( In fact, a template file is no more than a page ). If you want to display some posts you need to run a custom query or to include ( get_template_part() ) another template file which normally runs a query for some specific post types or categories.

Page template example

/*Template name: Example page */
get_header();
    /* The following loop refers to the page object */
    if( have_posts() ) : while( have_posts() ) : the_post();
        the_title();
        the_excerpt();
    endwhile; endif;

    /* Now you can query for your post using WP_Query Class */
    /* Defining $args array of arguments */
    $args = array(
        'post_type'         => 'post', // maybe page | custom post type | an array of these
        'posts_per_page'    => 6,      // number of items you want to display
    );

    /* Define new $query object to loop through */
    $query = new WP_Query( $args );

    //Start your custom loop
    if( $query->have_posts() ) : while( $query->have_posts() ) : $query->the_post();
        the_title();
        the_excerpt();
    endwhile; else: 
        echo 'No posts found';
    endif;      
 get_footer();

Let me know if you get stuck : )

Please, look these from WordPress Codex:

1. Templates
2. Stepping into templates
3. Template Hierarchy
4. The Loop
5. WP_Query

UPDATE

If you look at my example code you will see an $args array. You can define several options within it please refer to WP_Query docs.
Note: have_posts(); and the_post(); functions don’t accept any arguments.
If you want to use the in_category(); you have to do it in the loop.

Custom loop

if( $query->have_posts() ) : while( $query->have_posts() ) : $query->the_post();

  if( in_category( 6 ) ){
    //do something
  }else{
    //do something else
  }

endwhile; endif;