In addition to the security offered by HTTPS there are additional SEO benefits for webmasters to take advantage of.
More Referrer Data
Whenever traffic passes from a secure HTTPS site to a non-secure HTTP site, the referral data gets stripped away. This traffic shows up in your analytics report as ‘Direct.’ This is a problem because you don’t know where the traffic actually comes from.
If you use HTTP, traffic from sites like www.storylandnh.com shows up as ‘direct’, because StoryLand uses HTTPS. In simpler language your analytics may show a significant change in referrals from this site because they show as a direct link or / in your analytics report – rather than where the referral truly originates. If you pay for such a link it is important to be able to track the amount of traffic your investment returns.
If you have SSL on your website when traffic passes from an HTTPS site, the secure referral information is preserved. This holds true whether the original site uses HTTP or HTTPS.
As more and more sites make the switch, this becomes increasingly important.
HTTPS as a Rankings Boost
HTTPS sites receive a small ranking boost, but don’t expect a visible change. Google uses HTTPS as a positive ranking signal. This signal is one amongst many others, and currently carries less weight than high-quality site content; you should not expect a major SEO advantage for moving to HTTPS in the short term. In the longer term, Google may increase the strength of the HTTPS boost.
In fact, don’t expect HTTPS to act as a silver bullet – it’s becoming an important part of an overall SEO plan. If rankings are your only concern, there are likely dozens of things you can do that will have a bigger impact.
Check here for some suggestions – SEO Basics
From the horses mouth – more info from Google directly: https://support.google.com/webmasters/answer/6073543