Prompted by +Ben Huh
's question, I came up with this statement that contrasts +1 and Share:
+1 and Share are orthogonal: +1 is a signal to the original poster's circle that you 'like' it, while Share allows the original post (and only the post—none of the original comments) to go into other circles of your choosing.
So in terms of who sees +1's, it's like a content-free comment: mostly it associates your profile with the post or comment, and makes the post "fresher" (moving it to the top) in the circles that can already see it.
I get why Ben is scratching his head at it, though—before I tried to answer, I hadn't thought about it much, but it really is fairly different from Facebook. It's more "rational" (orthogonality of purpose) and respects privacy a lot more (though see https://plus.google.com/101935208782346638037/posts/AB2wHJRGPUs
by +Rod Begbie
for some complications) than Facebook, but as a result, it gets rid of the casual serendipity that comes from FB's general disregard for privacy.
(I think there's loads to discuss there, but probably best left for a different post.)