A web directory is, in a sense, a precursor to the search engine. Before crawlers got good (roughly the invention of Google in 1998,) and when surfing the web was something people did for fun, your best bet for finding quality content was a web directory. These were hand-curated, sometimes hierarchical lists of websites divided up based on topic. As far as I can tell the most famous and comprehensive of these was Yahoo, who paid a ton of people to just surf the net all day looking for cool web sites to add to the directory.
Unfortunately this method doesn't scale, and so as the web exploded in popularity web crawlers became a necessity in order to capture all of the pages worth viewing, and web directories, for the most part, died.