They contain lists of sites organized by topic or subject category. They usually provide a top level of broad categories. Click on one to get a list of subtopics in that category. You will encounter more lists of subtopics until you end up with a list of actual sites. Some directories include descriptions of the sites, some just provide the link to the site.
Many directories are also searchable.
EINet Galaxy Sites are arranged by subject category. A search form is included that searches all WWW pages referenced by Galaxy. This is an extremely comprehensive list of WWW sites arranged in an alphabetic list of subject categories. It cannot be searched. Yahoo Yahoo is probably the most popular and largest directory.