Scraps of Mystery are series of secondary sidequest that is a giant treasure hunt that takes you on a near-complete tour of Lucis.
Individual "Mystery Maps" that trigger numbered Scraps of Mystery quest are hidden in a very specific locations, with no prompt or highlight to draw your attention unless you are directly standing right next to them. They are, therefore, very difficult to find without prior knowledge of where to look.
Once you have a Mystery Map and select the assignment as you active quest. a search area will appear on in-game maps. You nust then head to the location in question and scour the terrain until you find the corresponding Sylvester's Map Piece.
Scraps of Mystery