Links are an important part of SEO. They are seen as a vote of trust from search engines like Google, Yahoo and Bing. In essence, a link is is a reference from one document to another.
Links go from a webpage to an internal or external website. By having links from high ranking external websites pointed at your website, search engines will look upon your site as having authority and relevence. This will help in the positioning of your website in serach engines.
The text that you use to link from is called anchor text. This is very important as it helps search engines understand where the link is going to. So, strong anchor text will describe where the link will take you. An example of how to use anchor text would be: "At Organic SEO Specialists one of our favorite blogs is about social media". The anchor text is "Social Media" and the link is going to our blogs about social media. Always remember to keep your anchor text relevent to the page you are linking to.
If your website has great content in the form of blogs, news or white paper reports you will attract links from websites wanting to reference your content and website. Link building isn't as easy as mass submitting to directories (which I would not recommend). It takes patience and work but if you keep at it you will steadily build up strong links that will help your websites positioning in search engines.