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)

The inventory has a certain capacity to store all the items you collect in the game. It can get full, but you have the ability to upgrade its capacity multiple times so you can stock more items and therefore earn more cents by collecting more items.

You can upgrade it by providing the Item required then tapping on the Upgrade button, or paying directly in Dollars if you want to skip this.