The inventory will ultimately show you the available pets and trainers, but will also serve as your Chibi Pad. With your Chibi Pad, you're able to upgrade, feed, and train your pet as well as download the 3D files, and look up the mission history.
Later you will be able to see resources as well as items that have been earned during a mission.
Clicking on a Chibi Fren will bring you to the detail page for each fren. In the following it will be explained how to use it to level up your fren.