In TwentyThirteen, there are many files, their names're started with content:
- content.php
- content-none.php
- content-aside.php
- content-audio.php
- content-chat.php
- content-gallery.php
- content-image.php
- content-link.php
- content-quote.php
- content-status.php
- content-video.php
Among them, except the first two, all the others are for different post types, and you can understand their usages from their names.
The 2nd one, content-none.php is used to display apology texts, when there is no content found with a query. And the 1st one, content.php is used in various display pages with two conditions, where:
is_search() — is to check whether it is the search result page
is_single() — is to check whether it is the post details page
If you open the index.php, you will find a code:
<?php get_template_part( 'content', get_post_format() ); ?>
Here the template part (content.php) is called.
Answer
So, to show excerpt in your front page or home page, you will need to modify content.php. Like the is_search(), is_single(), there are several other checkers in WordPress:
is_home() — is to check whether it is the home page
is_front_page() — is to check whether it is the front-page
is_category() — is to check whether it is the category archive page
is_archive() — is to check whether it is the general archive page
is_tag() — is to check whether it is the tags archive page
- ...so on
And you may know that, to enable excerpt instead of full content, you will have to change the code the_content() to the_excerpt().
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EDIT
Yep, @Rarst said a very important thing that, if you make change into any public theme, the changes will be wiped out when a new update will take place. So, to put your modifications in place, you have to make a Child Theme on TwentyThirteen. A Child Theme is nothing but a new folder with a stylesheet. You can get that at: