The SERP, or Search Engine Results Page, is the collection of links that appear after searching for a keyword.  The SERP is checked to determine the rank of a website for a keyword.

Older SERPs used to be a simple list of links and descriptions based on the content of a webpage.  Now, symantic intelligence in search algorithms allows for results to be customized based on the location of the search, news updates, social cues, or language cues.  For instance, searching for “Plumber” will show a list of nearby plumbers (based on where the search engine thinks you are based on IP geolocation) rather than general sites on plumbing.