Use minimize when you don't want to lose what's in a current window, but you do want to get it off your desktop for the moment because you need something else that's there. So it's minimized to the dock. For example, you're in Safari, but you're working in Word too, and you need space for a couple of Word's windows, so you put Safari into the background by minimizing it.
You close a window when you're done with it. You don't need what's in it anymore, but you're not done with the program that created it. Say you're in Word editing a document, you print it, you save it, and now you're done with it. So you close it. But unlike Windows, that doesn't make it quit Word, because you were actually going to work on another document, and if Word closed you'd have to launch it all over again.
When you're done with a window, you close it. When you're done with an application, you quit it. When you want to temporarily move a window off your desktop, you minimize it.
You can also hide an application's windows using command-H. It's still running, but all its windows are gone until you click on the application's dock icon again.
Hope that helps.