Snippet is a text cut by a search machine from a page and shown in results of the search query. Often, having evaluated snippet, one can roughly understand if the page matches exactly with your request without even opening this page.
The Google sometimes provides the text from the "Description" metatag as snippets.
The setting of snippets is an important stage in promotion of a site in search systems along with achievement of high positions in search results because it strongly influences clickability.