Citations are how your business name, contact info and address appear throughout the Web in places such as search directories. Having more citations than your competition used to be the answer to higher rankings but recent updates have increased the importance of inbound links, reducing the impact of citations. That said, citations are still a great source of links for your site and can be used as tiered links or for anchor text diversification.
Most businesses will have citations on the core directories like Yelp, Superpages, Angieslist and YP. Beyond the basics, you can also find numerous niche and location specific directories to list your business on as well. Bright Local has put together a tremendous location-based citation and niche citation list, check them both out for a ton of opportunities.