What are the extra prayers and what do they mean?

We pray 2 extra rakats after the morning prayer, 2 or 4 after duhr, 2 after maghrib and 3 after Isha. I always knew that they were extra and it's good to pray them but I don't know what they mean. Did Prophet Muhammad (pbup) used to do them and that's why we're doing them or did Allah (swt) say it's good to do them? Also what's the benefit? Any extra prayer is good of course, I'm just wondering if there is a hadith or something that will kind of clarify it for me.