The SERP Snippet illustrates how your page may be shown in Search Results for a particular query. Typically the page's Title, URL and Meta Description have been the main components utilized here, and hence could be carefully dictated, though Search Engines are more frequently building these snippets themselves to better represent the page content to their searchers.
It's important that the SERP Snippet is enticing for your searchers to click on, and accurately represents your content to avoid bounces or heavy re-writing by the Search Engine. You should keep these factors in mind when populating the page Title, Meta Description and URL.