Not much to work on. Maybe you said more than it looks like to me but ...

Sounds like it could be something like a window, or a tooltip, and there are a heck of a lot of items on a web page, and on toolbars. I can't tell a thing a from your description.

There's also page preview on Google search results, stuff that might be attached onto the cursor itself or left behind but not moved with the cursor when moved away from a link to a tab, or bookmark or other toolbar item or location. I am not that good at guessing. Perhaps you could provide a better description of what you see, when you see, what you expect etc., how to duplicate the problem. Maybe even how to fix the problem then everybody would better understand the problem and solution.

Is an image, is it text, what does it say or look like.

It is a box that has commands such as: Open in new tab open in new window etc;

If that is the wording it would seem to be from the context menu of a bookmark. There are a few extensions that try to save you time by showing stuff as you mouse over things that have very good context menus.

"Esc" key: may dismiss such things. The "Stay-Open Menu" is a desirable extension where use of the "Ctrl' key holds menu open until you click outside of the menu (particularly good for bookmark menus).

"Stylish" extension:  many styles can be installed to go with this extension

Test: disable Stylish with its toolbar icon (or extension options) to see if you still have a problem. Once had a similar problem with styles that had a scrollbar in their name and there may have been transparency involved, but those problems long since disappeared when Firefox got updated (before Fx4) with no changes to the styles.

Safe Mode: bring up in safe mode one time, when you do so do not check-mark any of the items (they are certainly not safe). Help ("Alt+H") > "Restart with Add-ons disabled". If there is not problem then it is almost certainly an extension.

• http://kb.mozillazine.org/Standard_diagnostic_%28Firefox%29#Extension_issues