A mystery for me in a game is generally something that even I am unaware of its potential. As a Games Master (GM) I love to be surprised in the game just as much as my players do. I try to include things in the games I run that I have not fully fleshed out for that purpose.
I picked this concept up from Apocalypse World and Dungeon World. They specifically demand that the person running the game allows themselves room to be surprised just as much as the players. In Dungeon World it is leaving rooms empty and asking the players what they see. In Apocalypse World, it can be largely anything. In both games the setting is largely created by everyone so the GM is surprised from the beginning.
I have other people in my gaming career that are big proponents of this concept. Stu, Dan, Scott and others that have shown me how good this can be. Though I have not stated it clearly here, this concept builds mystery in a game for me. It also builds it for the player because they can shape the game in the ways they want. Often this is by throwing something in that is a mystery they need to investigate. I now use Story Path Cards exclusively in my games to take this one step further. Allowing the players to take the game to unexpected and mysterious places. Give it a go and keep rolling!