About extended circles
When you share something, you might notice an option to share with your extended circles. Your extended circles include people in your circles' circles. Posts shared with your extended circles will be visible on your posts tab to people in your circles' circles.
For example, let's say Nediva is in one of your circles, and Jadon is in one of Nediva's circles. You don't know Jadon and he's not in any of your circles. If Nediva chooses to have Jadon visible on her profile among the people in her circles, and you choose to share a post with your extended circles, that post could appear on Nediva's Home page and be visible to Jadon on your Posts tab of your profile.
You aren't able to see a complete list of the people included in your extended circles -- it's a collection of people that's frequently changing.
Your extended circles may also be used to help generate suggestions of people Google+ thinks you may know.