A directory is basically a list of websites. Think of them like the yellow pages of the web.
Directories will link back to your site and Google decides who to place at the top of search results based in part on the number and quality of these “back links.” The really valuable part of being in a good directory is that they have what’s called a high PR score (Page rank score). So they not only link back to you, but their link is considered more important. The key thing here is to submit your site to a reputable directory. Submitting to every link directory out there may actually harm your SEO (Search engine optimization), because a lot of them are not considered good references. High quality directories on the other hand typically have a demanding submission process, this is why search engines value their listings.