If a group is private then you will need to use a special password to be able to retrieve feeds from it or use the Atom Publishing Protocol to contribute content. You will also need a password if you want to get the feed of your personal activity stream.
To create a feed password, click on the drop-down menu button at the top right of the screen next to your name, select the My preferences menu item and then the Feed access option.
If you just want a read-only feed, choose the Generate a new password for your private feeds option. If you want write access too so you can use the Atom Publishing Protocol then choose the Generate a new password for your private feeds and APP option. Now enter your password to prove you have permission to do this and select the Save button.
You will now be shown the details you need to authenticate with for the feed. Click on the Show password button to be able to see the password you will use.
Should the password ever be compromised or you simply want to stop a service from being able to use it, then come back to this preferences page to generate a new one or, if feed access is no longer needed, revoke the old one.
Note that if you change your main password then this will also revoke your feed password so you will need to set up a new one.