Organic Search Engine Optimization (or SEO) is the practice of maximizing a websites effect on search engine results in its market. SEO is a way of being known for specific products, services or information. The ultimate goal is to not only bring users to your site, but to bring the ones who are looking specifically for what you have to offer.
It used to be that a good url combined with consistent title and header tags was enough to rank high in the search engines (FYI - when referring to "the search engines", we are referring to Google, Bing and Yahoo. There are other engines besides these three, but none that really matter in the big picture).
Then Google came along with its algorithm, and all of a sudden search engine optimization became a social game. Years later, with the complexity of search algorithms increasing along with the tricks and tactics of internet marketers, SEO is no longer a brief list of best practices. There are many factors that contribute to ranking well in the search engines, and the term, Search Engine Optimization, has come to encompass them all.