"Sign in using your Google account" entries are automatically added when you use your Google account to log in to a website (such as a Stack Exchange site like this one) and leave the "Remember this approval" box checked. Any site in the approval list can know whether you are logged in to your Google Account and (if so) which account you are logged in to without asking you first.
According to Google, unless a site asks for additional permission, it cannot retrieve any personal information other than your e-mail address.
Any additional request would have been listed both on the original approval screen and in Google's "Connected Sites, Apps, and Services" list instead of just "Sign in using your Google account".
You can "Revoke Access" for a site if you do not want it to know you are logged in to your Google account without your explicit permission (or no longer want to allow it access to your account in a way you previously approved).
You will be prompted for your password. After that, you're shown a list of all sites you've used Google to authenticate with, and applications that have access to your account.
Best Answer
"i inside circle" is just a UI design. If you hover over mouse pointer or click on the icon, it will show all the related information.
This all is to warn the user for secure login or to use any third party app.