The units in your formation will quest at the selected stage.
As the number of stages increases, enemies that appear will gradually become stronger.
However, they will also earn you more Master Rank EXP, Zeni, and gear of a higher rank/grade.
Stages have a turn limit of 10 turns.
If you are unable to succeed by the end of the 10th turn, you will not receive any Master Rank EXP or items.
(There is also a set clear time for each stage. If you clear it faster than that time, the remaining time will simply become standby time.)