The original Yellow Pages style directories on paper were simply a way to look up businesses contact details and information. A Web Directory is similar in that it allows users to look up links to Websites.
Often these directories will be organised in a similar way to offline directories, splitting sites and businesses up into similar categories. Sites about plumbing will be grouped together just like the plumbers in the Yellow Pages.
Some directories are open and allow free submission of any site by the webmaster. Others are paid or specific to certain niches and sites must either pay or fit the rules of the directory in order to be included. Other directories will be more elitist and seek to only include sites of a certain quality or importance. Achieving a link from one of these directories can be extremely valuable as many of your competitors will be unable to do so.