Snippets, originally referred to the description of the page as shown below the title in a search on Google.  Google announced the launch of rich snippets on Blogspot on 26/08/2011 which extends the definition of the snippet to extract more structured data for particular types of pages.

Snippets are a few lines of structured text about the search result, offen displayed as bullet points.  This provides additional information about the target pages resulting from a search query.

Rich Snippets are extracted for particular types of information that lend themselves to more structured data, namely Products, Recipes, Events, Music, Reviews, People, and Businesses and Organizations. 

Google describes the results displayed as follows:
If a search result consists mostly of a structured list, like a table or series of bullets, we'll show a list of three relevant rows or items underneath the result in a bulleted format. The snippet will also show an approximate count of the total number of rows or items on the page. Google 28/06/2011

See also Rich Snippets for information on the Snippets format.