What is difference between 64bit and 32bit application?

I've read that 64bit apps use 64bit integer and memory addresses, and other stuff. I'm somewhat confused with this. I have vs2005 in my Windows Vista(x64), and i'm building an application that will be in x64 platform. When I checked the size of the integer(during debug mode), it's still only 4bytes(32bit). I'm confused. Can anyone explain to me this concept?

You can get general idea from this article.