Google will show +1 buttons next to all search results and ads, while encouraging other sites to include the buttons. All +1's are public and they're tied to Google Profiles. The goal is to use this data to personalize search results and ads by recommending sites +1'd by your friends. Google Social Search already does this, but there's no support for Facebook likes, so Google had to come up with a substitute.
"+1 is the digital shorthand for 'this is pretty cool.' To recommend something, all you have to do is click +1 on a webpage or ad you find useful. These +1's will then start appearing in Google's search results," explains Google.
This feature is slowly rolled out to Google.com, but you can try it by enabling the +1 search experiment.
One thing is clear: Google won't have to translate "+1" when it will localize the service, but it will have a hard time translating "+1's", "+1'd" and other cryptic constructs. Google +1's URLs already look weird (here's the homepage: http://www.google.com/+1).
Your +1's are listed in a profile tab, where you can manage them. There's also a page that lets you disable personalizing Google ads using +1's and other information from your Google profile.
Google now has the most important pieces of a social network (profiles, activity stream, likes, apps), but there's still no social network, no magic "glue" that connects the existing pieces. As Danny Sullivan explains, the "+1 social network" is made up of your Google Talk friends, the people from Gmail's "My contacts" group and the people you follow in Google Reader and Google Buzz, but you'll soon be able to connect other services like Twitter and Flickr. It's actually a meta social network, an artificial service that won't have too many enthusiastic users, just like Friend Connect.