Look in your theme’s folder for a file called “category.php”. Open it then look for something like this:
<span><a href="https://wordpress.stackexchange.com/questions/7088/<?php the_permalink();?>"><?php the_title();?></a></span>
Place this right below it:
<p><?php the_excerpt();?></p>
That will display an excerpt of each post below the title.