A secure website will store an encrypted or "hashed" version of your password (hashing is like a one-way encryption of the password so that the password cannot be deduced from the hash). This is done so that even the system and database administrators working at the website cannot work out what your password is.
Some websites are less secure than others though. One way you can be sure the website password system is insecure, is if you use the "forgot password" feature of the site, and the site sends you your password by email. If the site sends you a new password, it may be secure, but if the site sends you your original password, then that means your password was being stored in a database without any encryption at all. Avoid these sites if you can - if not, at least make sure that the password you use for that site is unique, so it can't be used to access any other website.
