How can I show post excerpts on the tags page?

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To show post excerpts on my tags page, you will need to make changes in content.php. By default content.php uses post excerpts for search pages only but you can modify the default behavior.

This is how you can include tag pages to show post excerpts. Add || is_tag() as follows:

<?php if ( is_search() || is_tag() ) : ?>
<div class="entry-summary">
  <?php the_excerpt(); ?>
</div><!-- .entry-summary -->
<?php else : ?>
<div class="entry-content">
  <?php
    the_content( __( 'Continue reading <span class="meta-nav">&rarr;</span>', 'twentyfourteen' ) );
    wp_link_pages( array(
      'before'      => '<div class="page-links"><span class="page-links-title">' . __( 'Pages:', 'twentyfourteen' ) . '</span>',
      'after'       => '</div>',
      'link_before' => '<span>',
      'link_after'  => '</span>',
    ) );
  ?>
</div><!-- .entry-content -->
<?php endif; ?>

If you want to use post excerpt for categories, tags and author pages then better use is_archive() instead of is_tag() in above code.