Some password fields have the autocomplete attribute set to 'off'. When Firefox encounters one of these fields, it will not offer to save this password in your password manager.
This can be annoying or undesired, and reallyremember lets you, the user, make the decision about whether you want to store the password or not.
When reallyremember is installed, any password fields marked with autocomplete='off' will be tinted a light blue colour. You can right-click on it and select "Remember this password", and reallyremember will remove the autocomplete='off' attribute from the password field.