The drop-down from the URL/Location/Address bar is suggesting items from your History and/or Bookmarks. To control what is displayed set the option at:

• Firefox button > Options > Options (or Tools > Options. using the Menu Bar) > Privacy > Location bar section (choosing "Nothing" will keep the drop-down from displaying)
• See --> Options window-Privacy panel

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Not related to your question, but...

You may need to update some plug-ins. Check your plug-ins and update as necessary:

• Plug-in check --> http://www.mozilla.org/en-US/plugincheck/
• Adobe Shockwave for Director Netscape plug-in: Installing (or Updating) the Shockwave plugin with Firefox
• Adobe PDF Plug-In For Firefox and Netscape: Installing/Updating Adobe Reader in Firefox
• Shockwave Flash (Adobe Flash or Flash): Updating Flash in Firefox
• Next Generation Java Plug-in for Mozilla browsers: Installing or Updating Java in Firefox

I have done all suggested above but it did not resolve the problem...

The instructions previously given are for the Location Bar (where you enter a web address for a site); your description "On the primary search bar in the middle of the screen.."

• See --> https://support.mozilla.com/en-US/kb/Location%20bar%20autocomplete#w_how-can-i-control-what-results-the-location-bar-shows-me

If the problem concerns Search Suggestions in the Search Bar (to the right of the Location bar), do the following:

• right-click in the Search bar input area (where it says "Google" or some other search engine), click "Search Suggenstions" to un-check it.
• See --> https://support.mozilla.com/en-US/kb/Search%20suggestions#w_enabling-or-disabling-search-suggestions

Have you double checked that on Options > Privacy > Location bar section, you have chosen "Nothing" and that the selection remains after re-starting Firefox?

• See --> Preferences are not saved

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Nothing you have suggested worked. Will go back to Explorer or another search. Thanks

• Click the (empty) input field on the web page to open the drop down list
• Highlight an entry in the drop down list
• Press the Delete key (on Mac: Shift+Delete) to remove it.

• http://kb.mozillazine.org/Deleting_autocomplete_entries

See:

• Tools > Options > Privacy > Firefox will: "Use custom settings for history" > "Remember search and form history"
• https://support.mozilla.com/kb/Form+autocomplete

The items that show up are search words that I have never used and never plan to use. Guess all I can add is good-by!!!

Only the Google search bar on the google.com site and the Google search bar on the Navigation Toolbar show suggestions that you need to disable if you d not want to see them. The search bar on the about:home page can only show saved form data entries and those can be remove from the drop down list with the Delete key.