Minimum System Requirements is a mostly self explanatory term. This term refers to the minimum specifications a computer needs to run a given software program.
Unfortunately this number is often just a filthy lie. Many times this number will represent the minimum system that they were able to get the program to start up on, not the minimum system that can actually use the program in any real fashion.
Further exacerbating the problem is the fact that most unaware PC users tend to have a dozen useless system tray and spyware programs running at all times, which tend to eat up most of that 32MB of RAM before the program in question can even get to it (but I just got this computer from Gateway a few years ago, it cost $2000 and I am still paying for it, it should run everything).
A good real world thing to do is to be sure and have at least double the system that the box requires, this is usually enough for most programs, except Age of Empires II which will have speed problems no matter how fast of a computer you have.
A smart consumer should also be aware of the different versions of Microsoft Windows, not all of them are compatible with each other.