signons3.txt stores saved user names and passwords. It also stores a list of sites for which passwords are never saved. The Options/Preferences dialog contains a UI to view and remove the passwords.
This file is encrypted to help prevent others with access to your computer from seeing your passwords. If you do not use a Master Password then having access to both key3.db and signons3.txt will give access to the passwords, so use a Master Password to prevent that.
Signons3.txt is used in Firefox 3.0 instead of the older signons.txt or signons2.txt file (the older file is left in the profile folder for backward compatibility). Starting in Firefox 3.5, signons3.txt is converted to signons.sqlite. 
Manually editing signons3.txt is not recommended because its contents are encrypted and there is a UI to do common tasks. It is possible though to copy a full name and password section from the file in one profile to another profile provided that you have the same key3.db in both profiles.
The file's contents are as follows:
#2e (list of domains for which passwords are never saved) . (site with a saved password) (name of HTML user name field or blank for HTTP authentication) (encrypted user name) *(name of HTML password field or blank for HTTP authentication) (encrypted password) (the domain of the log in form) (a filler line for future expansion, currently: '---') . (more entries like the one above)
This file can be moved to a different profile as long as it is moved with key3.db, which is the encryption key.
Deleting signons3.txt will delete your saved user names, passwords, and "never save" password (exceptions) settings. If your profile folder contains a signons.txt or signons2.txt file, it will be migrated into a new signons.3.txt file; otherwise, a new signons3.txt file will be created when needed.