A citation in this case refers to having your business details listed in an online directory. It literally means that your business is mentioned (cited) in the directory.
The main details include your business name, address, website, phone number (and to a lesser extent other contact details) and sometimes the opening hours. The benefits of being added to relevant and reputable directories is that it both helps your customers to find you and provides you with more visibility across search engines. Generally, the more citations you have, the more likely your website will rank highly in search results. This is because it provides your site with authority and credibility that you are a legitimate business.