When you create a Google account, Google enables an option that saves all your queries and the results you clicked on. The service is called Web History and it can be extended to all the web pages you visit if you install Google Toolbar.
Web History has many uses, but Google has barely scratched the surface by offering some basic recommendations and trends. Google decided to personalize the suggestions offered when you type a query on Google's homepage by adding searches from your history. Like in Firefox's search box, the historical queries are displayed at the top, but the major difference is that Firefox saves the searches on your computer, while Google saves them in your account.
In the screenshot below, you can see the suggestions provided by Google after typing [gm] in the search box: there are 5 suggestions from my search history (all related to Gmail) and 5 popular queries from Google Suggest.
Google doesn't provide a way to disable the suggestions from your search history, so your options are to log out, disable query suggestions from the preferences page or delete the web history.
Update: I don't see this feature in all my accounts, so it's not available to everyone.
Google Pixel review update: Two weeks with the Google phone
19 minutes ago