Google +1 is intended to allow users to share content and interests with groups of users easily - a bit similar to the 'like' button on Facebook. You can get an overview of it here.
There have been some quite negative comments about this function since it was launched in July 2012. Some users have reported that after the first few weeks they experienced a big drop in the traffic that Google + was sending to them. Another problem is that it's not available to people under 18, and these are among the biggest users of social networks - Facebook is available to people over 13, so there is a lot of competition there. It's also not very business-friendly, and doesn't always integrate well with other systems.
However, it hasn't been around for very long and it is too early to say how successful it will be. You can also expect that Google will make a lot of changes to the product based on feedback.