When we talk about social media and SEO, we are talking about two things that are pretty intricately woven together. How you do with social media can have a direct and heavy impact on your search rankings with just about any of the major search engines. Most of the conversations are pretty general and non-specific when it comes to actually how social media can affect SEO - it is just accepted that it does which leaves a pretty large gap from a marketing perspective.
So exactly what does have a positive effect on your SEO from a social media perspective? Well, probably first and foremost is the all-important number of followers. The greater the number of followers your Facebook page has or your Pinterest board has or your Twitter handle has is all directly related to your ranking in search results. If you have 200 followers on these three giants, you aren't going to beat the guy who has 5000. The search engines are pretty savvy though, and they have built in stipulations against the pure numbers so that people can't just "buy" followers somehow and not be actually servicing or interacting with those secondary tiers.
So you need to make sure the followers you have are gained naturally - you post valuable content, followers respond, you reply, and so forth. In this way, you are providing content in your various social media formats that is benefiting others - that gets the attention with regard to search engines. The more you keep interacting, the more followers you end up with and the higher you rank.
The content you provide on your social media sites needs to be high-value - stuff people want to see and read about. The more high-value your content, the more authority you have as it relates to the subject matter. When this happens, you start to get noticed by external sites who want to link to your content. The more this happens - diverse external sites linking to your content - the more authority you gain in the eyes of the search engine giants like Google, and the higher you climb in the ranks. As you continue in this manner, you are essentially building a brand for yourself and your content.
Another way you increase your authority and therefore your ranking is by getting people to share your content on the various sites. The more that people like and mark your page as a favorite, share and reply to posts, or re-Tweet your Tweets gets you favorable attention by Google, Bing, Yahoo,, etc. There are a number of ways to get this interaction going with your public - things like getting others to agree with you on an issue or subject and thereby liking your page, or liking your page if they want to see specific content - as you ask the question and they high like to respond, you climb. One of the great things about this method of growing organically is it is residual - the more people like your page the more followers you have from their friends seeing your content. It gives itself life in the process of growing.
All of your social media interaction doesn't necessarily improve your SEO, but you can see how it definitely has an impact.