Google's promotional video for the +1 button, above, explains the social feature thusly: "When you click +1, you're telling your friends, your family and the rest of the world, 'this is something you should check out!'"
I guess, then, the Google +1 button is similar to Facebook's "Like" button, which I have always thought a bit strange when you push "Like" as to something that is terrible. You post that you were just involved in a tradgic accident, and one of your friends clicks the "Like" button.
Instead of your "Likes" being posted to your Facebook profile, your +1's are collected in your Google profile and displayed when people within your Google social circle search for something you have recommended.
Here is how I think it works, if you opt in via Google Labs, you'll see a translucent +1 button appear to the right of your Google search results. When you mouse over the button, it becomes solid and you can click it. Each +1 is logged in your Google profile. There, you can manage what you've +1'd and choose whether or not you want to make this information public.
I do not know really how this benefits a law firm or lawyer except to ad the +1 button to your posts on your blog.
We will just have to see how it takes off.