The Models are the figures you'll have to build in each Stage or in the Hypercube. The ones obtained in the latter Mode can be Common, Rare or Exceptional. Once completed, you can either sell them for Cubes, place them in a free slot within the Base, or put them away in the backpack. Models placed in the Base will produce a number of resources, depending on their rarity and the Land Lot they're in. Depending on the Free Slot the model is placed in, it might produce Cubes or Gems.
To place a Model from the backpack, you'll have to access it and select it or tap on a free space in the Base. Once you've selected the Model, a grid will indicate where you can place it, and, once there, it will produce Cubes or Gems.