WordPress | Category Posts

<?php

// Put this in your template file
$category_ids = get_all_category_ids();
foreach( $category_ids as $cat_id ) {
    echo category_description( $cat_id );
    list_cat_posts( $cat_id );
}

// Put this in your functions.php
function list_cat_posts( $category_id ) {

    $args = array(
        'category__in' => $category_id,
        'posts_per_page' => -1
    );

    $cat_query = new WP_Query( $args );

    if( $cat_query->have_posts() ) {
        while( $cat_query->have_posts() ) {
            $cat_query->the_post();

            // Output each post in the category here using standard template tags
            echo '<h6><a href="">' . get_the_title() . '</a></h6>';
        }
    }

    wp_reset_query();
}

?>