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I heard it is supposed to create a story, like on Facebook. but I've never seen any content on my Google+ wall other than the posts by persons in my circles.
On Facebook wall we also see images or links liked by our friends, even if we are not following those pages or peoples.
+1 activity updates in the stream, also for Pages
When you +1 a post, people in your extended circles who also have you in circles may see this +1 "activity update" in their streams. They will only see the activity update if they had access to the original post. Activity updates may also be visible in Google+ search results to anyone who can see the original post.
You can control how often you see activity updates from certain circles as well as control who sees your activity updates in their stream.
Read how to control your settings: https://support.google.com/plus/answer/3113301?hl=en
See the screenshots in this Google+ post
By default, I think they show up as part of your profile on Google+. You should see a +1 tab with content that you have +1'd (is that a verb?)
There's documentation / marketing material about it here. I believe you can toggle some setting to have your +1s show up to people in your circles.
When you +1 a post, people in your extended circles may see it in their stream.
I just found this on Google:
+1 activity updates in the stream
When you +1 a post, people in your extended circles who also have you in circles may see this +1 "activity update" in their streams. They will only see the activity update if they had access to the original post. Activity updates may also be visible in Google+ search results to anyone who can see the original post.
