The big search field on the Firefox (desktop) new tab page is one of the most puzzling UI choices in that browser. It looks huge and important but is actually just a decoy and does absolutely nothing; as soon as you type a letter it just switches focus to the location bar.
And with a recent update, someone went through the trouble and made it sticky so that if you scroll down on the new tab page, it remains visible, obscuring the rest of your shortcuts, while being even more useless because it's right below the actual location bar. Mozilla, why?
@kianga just turn it off if it annoys you?