The "share" link is only displayed when you mouse over the search result, just like the "+1" button. When you click the link, Google shows the standard Google+ dialog for sharing content. Unfortunately, you can't "+1" pages.
I think it's a bad idea to replace the "+1" button with the "share" link. The "+1" button works as a social bookmarking tool: you're not only bookmarking pages, but you also help other people find useful pages (and they help you). When you "+1" a page, your action is not automatically broadcast to everyone that follows you, so you're likely to use it more often. The "share" link creates a Google+ post, so you might only use it to share important things.
It's not clear why Google didn't enhance the "+1" button from search results pages by adding the sharing feature that's already available for the regular "+1" button used by so many sites. This way you could both "+1" a page and share it with other people.