1. Characters need to seem real to be believable. Real people have memories. So do real characters.
2. Our behaviour is affected by memory - memory of what we did wrong, memory of what we did right and the difference between the two! Our characters should reflect this too. They're not going to get it right all the time (good thing too - no story there!) but do need to show they've learned from their mistakes. That is where memory comes in of course.
3. Your world setting will have rules and values it expects its citizens to live by. Your characters will know what these are, will know what special days and ceremonies there are, and will live their lives i obedience to all of that or be rebelling against it, but again your characters need to know and remember what these are!
4. We are shaped by our memories in terms of who we are and why we are the way we are. Our characters should be too.
5. We can be haunted by memories, especially of those we've loved and lost. Our characters should be too.