I'm using Windows 7 64 bit and have two versions of IE9 (32 and 64 bit) on my machine. Why are there two versions of IE9 on my machine? As far as I know, other browsers do not have two versions.
I believe that the 64-bit version is more about being forward-looking and compatible with webpages that might have high RAM usage. Some people like to use 64-bit browsers for various reasons, though it isn't the mainstream. However, most of the browser plugins are 32-bit, and so the 32-bit browser is provided as the default for compatibility with most websites.
Both versions exist because there are many third-party extensions and plugins that are not yet 64-bit compatible. If you need to use one of these plugins and you are running the browser in 64-bit mode, the plugin will either fail to work altogether with no error message displayed, or you will get an error message from the third-party plugin instructing you to quit IE in 64-bit mode, launch it in 32-bit mode instead, and reload the page that requires the plugin.
At this point it is practical simply to run IE in 32-bit mode all the time, even if you are running Windows Vista 64-bit or Windows 7 64-bit.
Since Windows supports 2 versions (32-bit & 64-bit), so it has provided two compatible corresponding versions of IE9.
Two versions of Windows is provided because the 64-bit version of Windows handles large amounts of Random Access Memory (RAM) more effectively than a 32-bit system. The terms 32-bit and 64-bit refer to the way a Computer's Processor (also called a CPU), handles information.
Also I would like to let you know that if the IE9 program / software is specifically designed for the 64-bit version of Windows, it won't work on the 32-bit version of Windows. (However, most programs designed for the 32-bit version of Windows do work on the 64-bit version of Windows.)
Hope it helps.