Google Sitelinks Explained
Selected web sites have been given Sitelinks on Google search result pages since awhile ago. Google Sitelinks are links that appear directly underneath the search result of a site and are determined by Google’s algorithms. Currently, Sitelinks are only shown for top search results.

Google usually shows 2 to 8 Sitelinks for a site.
Google usually gives Sitelinks to a web site for its main keyword in which in most case it happens to be the site’s brand name keyword. Sites that have limited daily search volume keyword on its main keyword are not given Sitelinks. The number of clicks of the site to that keyword may also be a factor.
Google seems to take a web site’s domain age into account, when considering Sitelinks inclusion for a website.
High number of backlinks pointing to a site with the main keyword in the anchor text also increases the chance for a site to be awarded Sitelinks.
By placing the links of your most important web pages close to the top of your site’s homepage increases the chance of those webpages being selected as Sitelinks.
Sitelinks are essentially additional links given by Google towards your site. It is important to understand how you can optimize your website to get this free offer from Google.
Recently Google seems to be testing another feature for selected top search results. A search box is placed right below the top search result of a site, if the site’s main keyword is searched. Certain selected sites get both Sitelinks and this new search box for their top search results, which in my option is stuffing users with too much information - the concept of directory and search at one place.

Hi Gordon,
I would like to add that sitelinks also are a sign of the website having an “authority” status, which means they have achieved a certain credibility threshold in Google`s eye .
I translate this into having a very good base to build on, if you are that website owner . Adding lot of content will draw huge traffic to your website as now your pages will be “sticking” much better in the serps.
Kris
[...] first introduced Sitelinks close to the end of 2006, but also introduced Site Search recently. Sitelinks below the top natural [...]