This error message can be from one of 3 problems:
1) You are out of hard drive space.
2) Incorrect permissions in your mozilla / firefox directory
3) A corrupt database,
So while many people advise you simply delete your firefox profile, that does not really address the problems and you will loose your customizations (bookmarks).
So, first , check to make sure your home or root partitions are not full. If they are, make more space.
Second, make sure your permissions are correct (this will fix any permissions problem in your home directory, firefox or otherwise).
sudo chown -R your_user:your_user /home/your_user
Last, if that fails, delete cert8.db
rm -f ~/.mozilla/firefox/*.default/cert8.db
For details see http://kb.mozillazine.org/Could_not_initialize_the_browser_security_component
One of those 3 steps should fix the issue without deleting your customizations.