A search engine allows people to find web pages/sites that contain a given keyword phrase. When a user enters and makes a query the engine returns the pages/sites that it determines to best match the search criteria. Each search engine has its own method of indexing a page/site to determine which ones rank best.

search engine types

• Web page search engine
  Indexes the content of web pages
• Web site search directory
  Indexes text descriptions for a site

Note that most public search engines, i.e. Yahoo, AltaVista, Lycos, actually use both a page search engine and a directory.

search engine scope

• External search engine
  Used to search pages/sites across multiple domains, i.e. Yahoo, AltaVista
• Internal search engine
  Used to search pages within a web site.

examples

The following is a list of popular search engines. Often these search engines are only portals to someone else's database. For example, Yahoo maintains its own directory for web site results yet uses Google for its web pages results. Yahoo used to use Inktomi for its web page results, which is used by Hotbot and others. Click here for a more exhaustive summary of top search engines.
 

• AltaVista
  Directory (by Looksmart) and search engine
• Excite
  Directory (by Looksmart) and search engine
• Google
  Search engine
• Hotbot
  Directory (by Open Directory) and search engine (by Inktomi)
• InfoSeek/Go
  Search engine
• Lycos
  Directory (by Open Directory) and search engine (by Fast & Direct Hit)
• Open Directory
  Directory
• Yahoo
  Directory and search engine (by Inktomi)

The above is just a list of a few popular search engine, there are literally thousands of search engines and directories on the Internet.