The default HTML page served by most web servers in response to a request for a directory. The name suggests that the page will contain some kind of index of the contents of the requested directory.
For example, if the content for website example.com is stored in the file system in directory /var/www/example.com, then a request for http://example.com/products would return the contents of file /var/www/example.com/products/index.html.
A website's home page follows the same logic. For the above example, a request for http://example.com/ would return the contents of /var/www/example.com/index.html.
It is often possible, and occasionally necessary, to specify index.html explicitly in the URL, as in http://example.com/index.html, though modern practice is to omit it.
Microsoft, of course, has to be different and uses default.htm instead of index.html. The variant index.htm is a throw-back to the days when some file systems only allowed three-character file name extensions.