A citation is otherwise known as a business or directory listing, a local citation is a listing that is relevant to your geographical location or country.
Citations will usually include NAP (Name, Address, Phone Number) amongst other information about your business which could be a description, logo, awards etc.
Citations make up part of a natural link profile. Individually they may not hold much link weight, but collectively citations will have a positive impact on your Organic and Local SEO rankings.