Hey SoniaS

It sounds like Firefox has gone through a refresh. Refreshing Firefox is quick way to fix commons problems and speed Firefox up, without losing any bookmarks, history or saved passwords (your extensions, themes, and some settings are removed). Firefox automatically offers to refresh itself if you haven't used it in a few days.

The "Old Firefox Data" folder is a backup of your old Firefox data from before the refresh. If Firefox is running smoothly and you haven't noticed anything missing, it would be a good idea to delete the old backup folder as it contains sensitive data.

There's more info about refresh here: Refresh Firefox - reset add-ons and settings

Thanks!

I just want to emphasize this part of the above reply: Before you delete it, please make sure you aren't missing anything essential in your Firefox.

As noted in the above article, Refresh removes settings and some add-ons, so the old folder may be useful for research/recovery if needed.