Pinterest can indeed have a positive effect on a site’s SEO. Google is rapidly moving towards using social signals very heavily in search results. In the video below, Maile Ohye of Google clearly explains how they are using social signals for Google+. You can infer that will be using these concepts for any social channel that makes its information crawlable, including Pinterest (skip to 14:00):
All search is moving towards personalized search. So, if someone re-pins something that links back to your site, you can expect your authority to increase in the SERPS for everyone who follows that person as well as for the people who follow the followers. You also have to let Google know what to rank you for by using keywords.
Pinterest can be fantastic for local SEO and market research as well.
Check out this post for more SEO benefits: 6 SEO Benefits of Adding Pinterest to Your Web Strategy