List all subcategories from category

Yes, you can use get_categories() using 'child_of' attribute.
For example all sub categories of category with the ID of 17:

$args = array('child_of' => 17);
$categories = get_categories( $args );
foreach($categories as $category) { 
    echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
    echo '<p> Description:'. $category->description . '</p>';
    echo '<p> Post Count: '. $category->count . '</p>';  
}

This will get all categories that are descendants (i.e. children & grandchildren).

If you want to display only categories that are direct descendants (i.e. children only) you can use 'parent' attribute.

$args = array('parent' => 17);
$categories = get_categories( $args );
foreach($categories as $category) { 
    echo '<p>Category: <a href="' . get_category_link( $category->term_id ) . '" title="' . sprintf( __( "View all posts in %s" ), $category->name ) . '" ' . '>' . $category->name.'</a> </p> ';
    echo '<p> Description:'. $category->description . '</p>';
    echo '<p> Post Count: '. $category->count . '</p>';  
}