The inventory has a limited capacity to store all the items you collect in the game. It can get quickly full, but you have the ability to upgrade its capacity multiple times so you can stock more items and therefore earns more cents by completing more orders.
To access your inventory, tap on the Menu button located on the bottom right corner of the screen, then on the Inventory button (blue backpack)
You can upgrade it by providing the Item required then tapping on the Upgrade button, or pay directly in Dollars if you want to skip this. Do bear in mind that if your inventory is full, you will need to create space by selling or deleting items, before you can use the skip button.