+1's are a social endorsement of content on the Google+ social network in the same way Facebook uses Likes and Twitter uses Favorites.
Why Do You Need to Understand +1s?
Users can click the +1 button on the Google+ social network to indicate they like a specific piece of content. However, the +1 button can also be applied to website or blog content, as well as ads from the Google AdWords platform. These endorsements are an important clue to Google as to the popularity, authority or relevance of a specific piece of content.