Inventory

The inventory can be accessed through this button:

After clicking on an item, the right side pane contains the item's name, the quantity owned, and a description of the item. The blue button at the bottom, when applicable, will allow you to use the item.

Inventory Top Row

Marriage Ring and Papers: For the provisional Marriage system.
Medals: Earned by clearing Extra Operation maps and Event maps. These can be exchanged for Remodel Blueprints or a pittance of materials.
Improvement Materials: Used in Akashi's Improvement Arsenal once you've acquired an Akashi
Morale Food 'Irako': Morale boosting desserts to boost ships to 'sparkling' status. Available through some Quests. See more at Morale/Fatigue
Present Box: Special drops available only during a certain time of the year.
Special Chocolate: Another item only available during a limited time of the year.
First Class Medal

Inventory Middle Row

Furniture Box Small: Contains 200 Furniture Coins
Furniture Box Medium: Contains 400 Furniture Coins
Furniture Box Large: Contains 700 Furniture Coins
Morale Food 'Mamiya': Morale boosting desserts to remove fatigue. Available through some Quests. See more at Morale/Fatigue
Remodel Blueprints: Blueprints used for some ship's Second remodel. Costs 4 Medals.
Furniture Fairy: Special carpentry fairies for building certain Furniture items.
(empty)

Inventory Bottom Row

Instant Repair: "Buckets" to restore ship HP to full instantly in the Docks
Instant Build: "Blowtorches" to instantly complete a ship construction in the dry dock.
Development Material: Item consumed when Constructing new ships or Developing new equipment.
Dock Key: Used to unlock additional repair docks and construction dry docks
Repair Team: Equipment used to prevent a ship sinking. See the Repair Team for details.
Repair Goddess: Equipment used to prevent a ship sinking. See the Repair Goddess for details.
Hishimochi or Saury: Special drop available only during a certain time of the year.