Anything selected has been picked. A selected prize has been chosen instead of other prizes.
To select is to pick something. When you shop, you make lots of selections. Something selected has been consciously chosen instead of other things. A selected duty is one an employee chooses to do, not one they're ordered to do. A selected penalty is one that is picked, not forced on someone. In a sports draft, the #1 pick is a selected player who was picked before everyone else.