That’s meant to give the program a chance to wrap up what it’s doing so that no important stuff gets lost or whatnot. So for example often enough instead of shutting down the program you’re greeted with a dialogue asking whether you’re sure about that or whether you want to save stuff or whatnot.
Now hitting the X, send a polite signal to shut down and usually the programmer can set for himself how to react to that signal, meaning the program can delay the shutdown and instead do something else before shutting down.
There are actually a number of kill signals that the operating system uses that range from politely asking to shut down to simply killing it no matter what trouble that is going to cause.
