By default Picasa Web Albums doesn't use any authentication, meaning you can only see public photos. However if you'd like to be able to choose from all your photos, public and private, then you'll need to enter your Google Account user name and password in this authorisation dialog.
Your credentials will be encrypted and stored locally and calls to Picasa Web Albums to identify you will occur over an encrypted https channel. In other words, your password will remain secure! As soon as you've authenticated with Google (and used the test button to make sure it works) you'll be able to add private albums for background selection.
See also: