Sometimes when I search for something on Google it shows some results (website links), but it also shows some important links on that website.
Is it a feature of the website or does Google use something to find those main links of the website? Is it related to search engine optimization?
Those are called "Sitelinks" and are automatically determined by Google.
While you cannot tell Google what URLs to use for sitelinks, you can demote URLs that shouldn't be used for that purpose. Much more information is available from Google Support on the topic.
See also: Official Google Blog: The evolution of sitelinks: expanded and improved
