Practice Mode

After you have cleared an area of a given dungeon and return to the world map, you will notice that you can now select single given areas. Doing so initiates "Practice Mode", as opposed to the normal "Story Mode" in which you explore a dungeon linearly.
In Practice Mode, a clock keeps track of how quickly you clear out the monsters and reach the exit of a given map. The world map display also tracks whether or not you have recovered the hidden treasure in that particular room, as well as your best clear time for that room.
Note that, unlike in Story Mode, you cannot advance the plot or "beat" a dungeon properly in Practice Mode; if you lose to a boss, for example, and then go back in Practice Mode to, well, practice, your victory will not advance the plot or unlock new abilities.
Treasure
Each individual area of a dungeon has a hidden treasure chest, in addition to a few you may find lying around in the open. The conditions you must fulfill for the chest to reveal itself, however, vary from area to area.
Should you manage to discover a hidden chest in an area, that area will be marked with a "Clear!" indicator on the world map screen.
Are there hints to finding the chests? You'll have to figure that out for yourself...