The site description information is stored in two places in the <head> of your site. In the “title” and the meta tag for “description”.
You manually add this information as straight info or using the WordPress template tags. All the information for both methods is in the article on the Codex:
http://codex.wordpress.org/Meta_Tags_in_WordPress
What Google grabs is up to Google. There are no garrantees. Sometimes this information comes from submitting your site.
Google does like to grab anything that you put in as a headline, too. For example, I have this at the top of my header:
<h1 id="header"><a href="<?php bloginfo('url'); ?>"><?php bloginfo('name'); ?></a>
</h1>
<h2 id="lowerheader"><?php bloginfo('description'); ?></h2>
And Google returns my blog name in bold followed by my blog description. Google tends to ignore meta tags, because they were so overused by spammers, but it might use a description meta tag.
