Inventory is the space the player has to hold items. How items are stored and where depends on the type of item. Quest Items are unique, there can only be one held at a time - and there's a special inventory section under the Status menu next to weapons which displays the currenly held Quest Items.
Food which is either purchased or cooked is stored in the main section of the Inventory menu. The number of slots available here can be expanded by purchasing backpack upgrades, allowing the player to hold more items. The main area of inventory also displays stat info and descriptions about items when selected, and shows special currency collected and heart pieces.
There's also the ability here to edit the 'Fast Switch' menu for quick weapon access.
Inside the inventory menu there is another section, which can be accessed by selecting 'Backpack' and toggling right. This is the Ingredients inventory. The player can hold up to 9 of each unique ingredient before running out of space. This inventory is accessed when interacting with a cooking station.