When you run a program, Windows sets up an environment in which to run it (I mean in terms of memory, addressing, etc., not just environment variables). This environment depends on the contents of the executable (32-bit and 64-bit programs differ internally). When you run a 32-bit program on a 64-bit system, it runs in the 32-bit subsystem which emulates a 32-bit environment. It is called WoW64WoW64 (WoW64 stands for Windows on Windows 64-bitWindows on Windows 64-bit) and is similar to how 16-bit apps would be run in XP using the NTVDMNTVDM.
(I am using a different computer, so I cannot rely on my browser history to backtrack my steps, but the other day while answering this SU questionthis SU question I ended up at this SO question which caused me to Google PROCESSOR_ARCHITEW6432 which lead to this SO question and this Microsoft blog postingthis Microsoft blog posting.)