First, search engines are changing their valuation of sites that have a significant amount of likes/tweets/plus-ones/etc. From the perspective of the search engine, these validations are actually far more relevant/valuable than "backlinks" (which is an older way of increasing your SEO rankings by getting other Web sites to post links back to you).
Second, to ensure that you are capturing as much of this Social SEO as possible, you need to make your Web site "social optimized" so that your visitors can easily share it. This includes embedding share buttons and ensuring that your meta tags include the right descriptions/photos for sharing (i.e. so that the right images and words appear in the description of your page when people share it on Facebook). This way, you can capture as much Social SEO as possible.
Third, it is important to encourage visitors (as well as your team) to share your site often. Yes, this will help with the SEO rankings, but more importantly it will expose your brand to the friends/audiences of those who share it. In this way, you can transform customers into salespeople for you.
All that said ... if your only purpose in pursuing this is to get higher placement in Google, forget about it. Search ranking is an only an outcome. The deeper purpose should be to focus on building relationships with customers through which they are invited to be a part of your brand (in this case, by sharing your site with their friends/followers). If you focus on that, the rest will follow.