Facebook rolled out a new feature for its search box “search suggestion,” – aimed at helping Facebook users to quickly find and connect with people, pages, groups, events at applications on Facebook based on user’s preferences. You’ll see results not only of people, events, groups and Pages you're connected but also friends connections. You'll see a relevant results and be able to discover new connections as well right as you're entering your search. The drop-down menu, let you go to the search results page by selecting "See More Results" from the bottom of drop-down menu. You'll be then taken to full results, where you can sort by different categories and refine your search further.