So Google +1. There seems to be a lot of "buzz" about it recently, though it's been available (experimental) since March. Google is now unleashing a brand new wave of changes in their next evolutionary step. It's all apart of what they are branding the Google + Project. It has some great looking potential but currently it is in beta and only open to invitation, which unfortunately has maxed out. What is publicly available is their "+1" button.
So…
What is it?
The easiest way to explain is that it's a lot like facebook's "Like" button. It has differences but many are saying this is Google's direct competition with Facebook and they are attempting to overtake the social media giant.
How does it work?
You will need to create a Google profile. Your profile is visible to anyone in addition to all connections associated to your gmail address. Whenever you are signed in and you search Google you will see +1 buttons next to indexed listings. If you like something, you can simple +1 it from Google (see sample below) or from a web page itself (see share links to the left of this article).

Your +1’s are stored in a new tab on your Google profile. You can show your +1’s tab to the world, or keep it private and just use it to personally manage the ever-expanding record of things you love around the web. If you are logged in, your +1's will show next to listings you have +1'd before, so you can tell websites you prefer over sites you do not.
Why does that matter?
People are more interested in things that friends like or approve of. If I'm going to buy a new product., I'm more interested in what my friends think of it than a paid actor on a commercial. The point is to "help people discover relevant content".
How does this affect my traffic and search performance?
Google doesn't explicitly say one way or the other but what they do say is:
"Content recommended by friends and acquaintances is often more relevant… Because of this, +1’s from friends and contacts can be a useful signal to Google when determining the relevance of your page to a user’s query. This is just one of many signals Google may use to determine a page’s relevance and ranking, and we’re constantly tweaking and improving our algorithm to improve overall search quality. For +1's, as with any new ranking signal, we'll be starting carefully and learning how those signals affect search quality."
I believe as Google continues to compete with Facebook, +1 will gain weight with search results.
Even if it turns out that Google decides that +1 will have no negative or positive effect whatsoever on queries, the amount of +1's and who they are from can play a big role in in tipping the scales for what users will click, read, buy, etc.
I would check out a website that has 200+1's over a site with none. Further still, I'd follow a link with a couple +1's from people I know than one that has more from people I don't know but still preferring both of them over a website with 0.
The Future
Google is very big and they have a lot of smart people on their team. They aren't infallible but I do think they are on to something with this, especially with their upcoming public release of the Google + Project . Don't be surprised to see that little +1 button more and more. So go ahead and get ahead and start using the +1 button. While you're at it, you should +1 this article.