Units can be fused together to produce experience, which will result in leveling up. In the home screen tap at the "units" page at the bottom and then tap "enhance units" in the next menu. Choose the unit you want to improve then select the next unit you wish to use as a "material" in the fusion process, ending the technique by tapping "Fuse".

You cannot enhance max level units with this trick.

Some max level can be "awakened" to produce for a much stronger product. Tap on the "Units" option in the menu, then find "Awaken Units" and select the desired unit you wish to upgrade. Tap the "Awaken" button to end the trick, but note that you have to the right quantity of material units.