You can backup files like these in the current Firefox profile folder to backup specific data. You can copy files like these to the current Firefox profile folder to recover specific data.

• bookmarks and history: places.sqlite
• bookmark backups: JSON backups in the bookmarkbackups folder
• 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
• cert8.db for stored intermediate certificates (Certificate Manager)
• persdict.dat for words you added to the spelling checker dictionary
• permissions.sqlite and possibly content-prefs.sqlite for Permissions and Site Preferences
• sessionstore.js for open tabs and pinned tabs and tab groups

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

• http://kb.mozillazine.org/Profile_backup
• https://support.mozilla.org/kb/Backing+up+your+information

These add-ons can be a great help by backing up and restoring Firefox

FEBE (Firefox Environment Backup Extension) {web link} FEBE allows you to quickly and easily backup your Firefox extensions, history, passwords, and more. In fact, it goes beyond just backing up -- It will actually rebuild your saved files individually into installable .xpi files. It will also make backups of files that you choose.

OPIE {web link} Import/Export extension preferences