Search suggestions help you to find out common phrases that other people have searched for. The search suggestions are offered by the search engines (such as Google, Yahoo, etc.) and not by Firefox. Firefox merely retrieves the search suggestions from the search engines, and displays the list to assist you in selecting a search phrase that has been used by many other users throughout the world before.
To enable or disable search suggestions through the Search Bar:

To enable or disable search suggestions through the Search Engines Manager:

To use search suggestions, start typing in the Search Bar, and wait a moment when you want the search suggestions to appear. Firefox will present you a list of search suggestions sorted by a decreasing order of relevancy.
To select a search term from the suggestions:
Search suggestions are offered by search engines, whereas search history auto-complete results are offered by Firefox by matching the entered search terms with the terms you have previously searched for.
The search suggestions list is marked with the word Suggestions at the top right corner of the list to make determining whether you are viewing search suggestions or search history simple.
If the list that appears does not have the Suggestions title at the top right corner, the list consists of only the search history.
If the a search terms matches items in the search history, and triggers search suggestions as well, a mixed list is displayed. The mixed list is divided into two sections by a horizontal line. The items above the horizontal line indicate search history items, and the items below the horizontal line indicate search suggestion items. Firefox is smart enough to filter the search suggestions result to exclude the items in your search history, so that the presented list does not contain duplicate entries in the history and suggestion items.
In some cases, search suggestions may not appear even though you have enabled them. Several causes may result in this:
Not all search engines offer search suggestions. Here is a list of search engines that are included in Firefox by default and support search suggestions:
Other search engines that you may add may or may not provide search suggestions. The easiest way to find out is to select the desired search engine, type in a term that you're certain that the search engine would be able to provide suggestions for, and wait a moment to see whether search suggestions appear or not.
Sometimes, the search term you have entered may be too specific (e.g. "firefox support article about search suggestions") or simply invalid (e.g. "dsjkyfsdakjfdjsyfyf"). In such cases, the search engine may not be able to provide any suggestions for the entered term.
Behind the scene, Firefox needs to contact the search engine's website, and request a suggestions list dynamically when you type a search term. If there is a problem in your Internet connectivity, Firefox will not be able to perform this action, so no search suggestions would be available.
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