In this case, Flickr wants the permission to post photos in Blogger Beta. Until now, when you wanted to send photos to Blogger you needed to enter your username and password. The new Blogger uses the same authentication like the rest of Google services, so giving you credentials means giving access to Gmail, Search history, Checkout, that store sensitive information. Of course you trust Flikr and you know they don't store your information or use it for dubious purposes, but the new authentication system sends you to Google when you need to enter your password and gives access only to one service (in this case, Flickr has access only to Blogger, not other services). If you want to, you can disable access for a web site at any time.
Hopefully, other sites like Meebo or Netvibes will use the same system, so you don't have enter your Google Account credentials if you don't see google.com in your address bar.