This is a really good question! However, the answer can be found relatively easily with a site:stackoverflow.com "A language-independent collaboratively" search.
The first thing you need to know:
https://support.google.com/webmasters/answer/35624?rd=1
We use a number of different sources for this information, including
descriptive information in the title and meta tags for each page. We
may also use publicly available information—for instance, anchor text
or listings from the Open Directory Project (DMOZ)—or create rich
snippets based on markup on the page.
If a description meta tag is not found for a page, Google will look for a snippet in content or in other places. Much of the time, it depends upon upon the search query. Since this is clearly a brand search for a known brand, it is likely that a different set of criteria are applied as opposed to a term based search.
This SERP snippet comes from DMOZ.
http://www.dmoz.org/search?q=stack+overflow
See item #2:
Stack Overflow - A language-independent collaboratively edited
question and answer site for programmers.
I did a few other searches and checked JavaScript and looked for mark-up, however, nothing showed up. The only place I found a source for the SERP snippet was DMOZ.
For what it is worth, it seems this question has been asked on StackOverflow: https://stackoverflow.com/questions/3796793/how-to-programmatically-provide-site-structure-and-url-path-to-google-search