Google has been quite open about what Google+ does for SERPs. It says that it will improve the rank for any of your friends who search on a term, so if you search on "widgets" and +1 a page, then one of your Google friends search on it, they are more likely to see your +1 page.
They don't provide data on exactly how much influence it has, only that they say it a small factor as it is new.
There's been some research done that suggests a 20% increase in visibility - google "rankings google +1".
Also, check out the integration of the Google +1 information in the Google Webmaster tools - it tells you how much effect the +1 button has had for you.
For any of it to work, of course, someone has to +1 you.