When you browse net and read various articles then you might see the Tweet, Facebook like, Stumble Upon button after the post. But at present time you may see another button with other sharing buttons. This is +1 button.
The +1 button is nothing but an alternative to Facebook like button. But don't think it just like Facebook like button. It is something more than Facebook like button.
When you +1 something actually you're doing many things. Give a +1 to a post means you're recommending this post on Google Search, Sharing with your friends in your Google + Circle and most importantly you're saving the page in your +1 list.
In order to use the Google +1 button, you must have a Google Account. And the account should be visible to public. If you don't set your profile publicly visible then you will not be able to see and use +1 button.
Sometimes you may wanna save a copy of your favourite web page. But you don't need to do so if you use +1. If you see a +1 button in that web page then just give a +1 and you will find this page in your Google + profile at the +1 list!