What is puzzling, philosophically, about possibility and necessity?

There is a problem which all philosophers must face—that of possibility and necessity.  “What problem,” you may ask, “I see no problem.  Some things are possible, like what color shoes I wore today, and some things are necessary, like 2 plus 2 is four.  What more do I need to know?” Ahh, there lies one problem: what do we know about possibility and necessity, because it seems that we know a lot about them.  That is the epistemological problem.  Another problem is the metaphysical one: what is the nature of possibility and necessity?