SEO Citations are references or mentions of your person, business, or organization on the internet. They may or may not have links to your site; it is the referencing itself which makes the difference for SEO.
The reason references are important, particularly for local SEO results, is that search engines rely heavily on citations to verify the identity of businesses. For example, if you are a local plumber, and your business is referenced on the local Chamber of Commerce site, several other local businesses, and some directory sites specific to your area, Google & Yahoo will have a much easier time helping people in your area realize that yes, you are a plumber, and that you are also in your area.
Citations also help deliver the impression to others that you are legitimate member of your local business community, which can be extremely important depending on which niche your business is in. The better ranked and higher traffic any given site has, the better candidate it is to pass link juice on to your site by way of citation.