The days you can look back on and think, "i miss it so much." or, "what was i thinking? i'm glad it's not like that anymore."
When most people talk about the old days, they discuss good memories with old friends. Sometimes, this topic can become very emotional and sometimes awkward (depending on the topic).
The old days are the days that are gone and done for. They won't come back. You could try, but nothing is or ever will be exactly the same as things were in the past. Even if they come very close. But the past is the past because it's over with. And there's nothing you can do about it, no matter how hard you try.
Person #2: Oh yeah, god, i miss the old days.
Person #1: Remember when Mark pushed you down the stairs?
Person #2: Uh, let's not talk about the old days..