Soon, according to [Web Link this Google video], the button will begin appearing on websites everywhere, much like Facebook's "like" button.
Google says that by clicking the button you will be telling your friends and colleagues which link they ought to click and that you will be able to see which links your friends and colleagues think you ought to click. If you trust that friend or colleague, well, then they've just helped you out, haven't they?
It's kind of like a little sticky note on your computer, or on the fridge, giving you a heads up.
Of course, the button is not only about making it easier to find the things you will probably enjoy online. It will also help Google deliver even more finely tuned targeted advertisements. Heck, they are even going to let people +1 ads they like.