There are a few kinds of links, some of which are more important than others for SEO. All of which you should know about and use strategically. There are:
<a> links - these are the majority of internal and external domain links. They show search engines the value and relevance of the destination.
Img links - alt and title tags are a way to leverage images as a link strategy.
Rel links are canonical tags that may be part of an HTTP header. Only time you really use this is if you want to pick a URL to index/not index.
NOTE: I am purposely not talking about nofollow links here because it's too deep for this discussion. Another time.
Links and Search Engines
Links are valued by search engines. As the Google bots crawl, index and rank, they use links to discover new pages and measure existing pages. High quality pages will improve in rank. Highly connected pages will do even better. This means that linking is an SEO ranking factor. It is inherent in the Google algorithm. Links are about your authority and confidence.
Now, there is a warning here: every time Google updates it refines its measurement of links. This is partly because people over-optimize their pages and use no-no techniques (like web directory listings in exchange for links). Practices like this get you penalized. But if you're a novice, you probably don't know enough to worry about that. No shade.
Link Building and PR
As much as responding to every comment on your Facebook thread is a vital tactic to growing your brand, link building is another aspect of PR you can't ignore. It's a less icky version of "like for like!" "follow for follow!". Wink. Shudder. Link building helps you build relationships. It forces you to get extroverted and reach out to other blog writers and entrepreneurs. You can promote the content you create and build long-term relationships with people who can help you grow your brand.
Link building also gets you referral traffic. It's earned, not paid. And the traffic you get from links out there is organic, which is the best kind of food to eat, I mean traffic to get.
Link Building Bonus Tip
Before you go scattering your blogs like seed in the wind, let me remind you: a good linking strategy begins with having something worth linking to. Don't disappoint the Google Bots by having garbage to drive people back to. Everything you write should accurately reflect your brand, provide value to the reader and be well crafted and thought out and I didn't really consider how to end this sentence.