The Search Box is basically an all-purpose search box.
It can search the current document, all open documents, menu items, help items, and, if enabled (as sending queries online is a privacy concern), online help items, tutorials, and commands from downloadable extensions. If the list of search results is too big, it’ll get a scroll bar.
When you push one of the “find” arrows (the ones you use to search the document), all of the command suggestions will get hidden under an expandable menu so that you would see more of the document.
(Oh, and it’s accessible with a keyboard shortcut. And you can use the arrow keys along with enter to navigate through it.)