Search engines are automated computers owned by companies such as Google, that constantly surf the internet 24 hours a day. These computers run programs called "robots" or "spiders". They archive, analyze and catalogue all of the pages they encounter. Then they add these pages to it's database or "INDEX".
For a great explanation of the basics of search engines, please visit the University Libraries of Albany.
What are Search Directories?
Search Directories perform the same function as search engines but they do not use computers to rank pages, they use people. People visit the submitted site and approve the site to a relevant directory. Yahoo is the best known search directory, although alot of people confuse it with a search engine.
For a great explanation of the basics of subject directories, please visit the University Libraries of Albany.