From MozillaZine Knowledge Base
The profile folder is a folder on your computer that stores your Mozilla application user data such as preference settings, passwords, extensions, themes, Firefox or SeaMonkey bookmarks, and Thunderbird or SeaMonkey mail. It's a good idea to periodically back up your profile to safeguard your data, in case something happens to your computer. Make sure to keep the backup not on the same disk (or even computer) as your profile folder, to avoid it being lost along with the profile in case of disk failure (or theft). This article describes how to back up your profile and restore it.
If you want to move your profile to a different place on your computer (or a different computer), see Moving your profile folder. It has different (and more complicated) instructions because it has to tell the application where the profile is stored. See Transferring data to a new profile if you're trying to recover data from a profile to reuse in another profile.
If you're migrating from Windows to Linux see this article instead.
Third party profile backup software
Recommended: If you're a Windows user and want a simple way to back up and restore profiles, it's recommended that you use the MozBackup program. MozBackup is a profile backup utility for Mozilla Suite, Firefox, and Thunderbird. This eliminates the need to find where your profile is stored, and it has options to back up just part of the profile. Its also a very convenient way to migrate a profile to another computer (or restore a profile on a reformatted boot disk).
If you're using Portable Thunderbird or Portable Firefox Mozbackup won't back up your profile because it expects to find it via the profiles.ini file, and one of the goals of portable applications is to avoid having to register and install the application on each PC. Portable Apps Suite (Base Edition) includes a PortableApps Backup utility. Toucan is a stand alone utility with more options, that lets you synchronize, back up and secure your data. It also supports command line arguments.
See this article for other alternatives, including automated online backup.
Manually back up the profile
If you are comfortable with copying files and folders you can manually back up your profile. This process can be as simple as copying a single directory to a backup location. Most of the work is in finding where the profile folder is stored.
Mail is stored by default within the profile. If you re-configured Thunderbird, Mozilla Suite or SeaMonkey to store an accounts messages outside of the profile, you need to also copy the "local directory" for that account. Look in Account settings to find the location of each account's local directory.
Manually restore the profile
To restore a profile backup:
In some situations you might want to manually back up or restore only certain files in the profile folder. See Transferring data to a new profile for a list of suggested files.