If a Firefox profile was reset, or refreshed, the old profile is moved to the desktop in case it is still needed. Did you do a reset?

https://support.mozilla.org/en-US/kb/recovering-important-data-from-an-old-profile

https://support.mozilla.org/en-US/kb/back-and-restore-information-firefox-profiles

The Old Firefox Data folder is created when you use the Refresh feature. During an update, you sometimes see a message that Firefox is starting or running slowly, and you can speed it up by restoring some default settings. If you click that button, the Refresh feature creates that folder.

More info on what you keep and what you lose in a Refresh: Refresh Firefox - reset add-ons and settings.

If nothing critical is missing then you can delete that folder, but I suggest giving it a few days just in case you need something and you haven't noticed yet.

Did you had a special reason to use a refresh to create a new profile?

What issues did you have in your previous profile?

Firefox should recover these by default:

• bookmarks/history: backups in the bookmarkbackups folder and possibly places.sqlite if you really need the history
• SQLite files like cookies.sqlite (cookies) and formhistory.sqlite (saved form data)
• logins.json and key3.db (decryption key) for Passwords saved in the Password Manager

You can copy files like these to your current Firefox profile folder.

• permissions.sqlite and possibly content-prefs.sqlite for Permissions and Site Preferences
• cert8.db for stored intermediate certificates (Certificate Manager)
• sessionstore.js for open tabs and pinned tabs and tab groups
• persdict.dat for words you added to the spelling checker dictionary

You can recover more personal data.

• https://support.mozilla.org/kb/Recovering+important+data+from+an+old+profile
• http://kb.mozillazine.org/Transferring_data_to_a_new_profile_-_Firefox