Custom Sidebar only on single post

In additon to wordpresser answer, you can also call to get_sidebar(‘sidebar-aside-content’); only in the template files where you want the sidebar be displayed. For example, if you include

<?php get_sidebar('sidebar-aside-content'); ?> 

in “theme_folder/single.php” file, the sidebar will be displayed only in single posts.

For example. In functions.php:

//Register your sidebar
add_action( 'widgets_init', 'my_widgets_init' );
function my_widgets_init() {
    register_sidebar( array(
    'name' => __( 'The title of my sidebar', 'curioso' ),
    'id' => 'sidebar-mysidebar',
    'description' => 'An optional widget area for my sidebar',
    'before_widget' => '<div id="%1$s" class="widget %2$s">',
    'after_widget' => "</div>",
    'before_title' => '<h3>',
    'after_title' => '</h3>',
 ) );
}

Now you have to create a file named sidebar-mysidebar.php and put it in you theme folder. This file will load the widgets. For example:

 <?php if ( is_active_sidebar( 'sidebar-mysidebar' ) ) : ?>

   <div class="mysidebar">
    <?php dynamic_sidebar( 'sidebar-mysidebar' ); ?>
   </div>

 <?php endif; ?>

Now in the file of your theme where you want ‘mysidebar’ be displayed:

<?php get_sidebar('mysidebar'); ?>