The Mystic Chest can be used for storing ships while they are not being used. The Mystic Chest starts out being able to hold 2 ships, and can hold 1 additional ship for each level it is upgraded. Each upgrade costs 100 gems. Fully upgraded, the maximum number of ships that can be stored in the chest is 21.
When a ship is put into the Mystic Chest, all weapons loaded onto the ship are also stored. The ship retains its level and all other characteristics.
Putting a ship into the Mystic Chest does not free up the crew to be used on other ships.