GeeMail actually the same with GMail. But this is running on the computer desktop as an application.
GeeMail is an email client application that running on Adobe Air (.air extension). To be able using it, you have to install Adobe Air first. Adobe Air applications (rich internet applications) is a web-based applications that can run on the desktop without requiring the web browser. This is free and running cross platform operating systems.
And GeeMail application makes GMail (Google Mail) is on your desktop.
It runs like you to use GMail with a web browser.
See some screenshots below.
Interested in trying?
Alternative application: Adobe Air application: GMDesk.