Google users have been asked for some time to establish a Google Profile. A little autobiographical sketch that you fill in. You've had an option to set that to Private but as of August 1, all private profiles will be deleted, so you'll need to make it public or lose it. Does this have to do with Google+? Of course it does! EVERYTHING at Google has to do with Google+ now. Welcome to the future. Here's your jetpack.
It should be noted that Profiles are different from regular Google accounts, like you might have if you use Gmail. Those can be as private as you like.