This introduction makes us realize Google always keeps watching user trends – the way people search the net. Google has found that many searchers first search for the website name and then move on to a more refined search. Say if you wanted to search for YouTube video upload info, you can first search YouTube in Google search box which would give you something like this
Which you can further refine by searching upload videos in the site search box
Oh. Yes you are right. It is just one of the features you can see in Google advanced search. Google helps searchers to have these kinds of refined searches in an easier way.