Google Reader is one of the many online feed readers that don't support authenticated feeds. This special kind of feeds requires a username and a password before displaying the content to protect sensitive information. An example of authenticated feed is Gmail's feed for unread messages, but you'll also find password-protected feeds for internal bug reports, private email distribution lists, etc.
FreeMyFeed wants to solve this problem by creating feeds that don't require authentication. The site acts as a proxy between the original feed and your feed reader, while promising that your credentials are safe. "Usernames and passwords are never stored on the server. The usernames and passwords are only parsed to retrieve your RSS feed and then are discarded." Rob Wilkerson explains that the credentials "are encrypted using a rotating algorithm and included in the new URI."
It's not a good idea to enter your username and password in any other place than the site where you created them, but FreeMyFeed could be useful for feeds that are not tied to important accounts. Make sure you don't share any item from the generated feeds.