1. A web site starting point to other pages and considered the index, or core page. When visiting a web site, most visitors will look at this page first as it often has news, information and changes more often than other pages.
2. "Home page" is old internet jargon for the first web page you see when you open your web browser. In the days of Mosaic, this pointed to the NCSA web site, which listed a number of other famous and useful web sites on the web. It was the main launching point, or root, to the web for many users.
Browsers have always allowed users to change the home page to any page they desire. Most browsers have a special "Home" button that instantly takes the user back to the web page they have stored as their home page. Many companies have taken advantage of this and attempted to provide home page services, often customizable portal web pages, that people can set up as their home.
As web pages got easier and easier to develop, many individuals began to create their own personal sites. Some of these users set their personal sites as their home page, so they could immediately access all their other favorite links from it. As this became more and more popular, the word "home page" came to act as a synonym for "personal web page", and is still frequently used in that context today.