A directory website is similar to a phonebook. It is done by submitting your URL and some company details to a directory site and the directory site reviews the validity of your link. Once a directory approves of your link, your website will be placed on the specific category of your business.
Directory submission does not have much effect in Search Engine Rankings. However, directory submission increases your website's visibility on the internet, more like free advertising. A directory usually has over 500,000 users, which is still a big number even if you assume that only 1% of the users will see your site on the directory.