The goddess' Level increases as they participate in battle, making them stronger.  The goddesses' max. level will increase as your guardian level increases.

The other way to increase their level is by using EXP potions. These are acquired either from battle or guardian chests.

Star awakening is another form of making your goddesses stronger. It can be accessed from the Awaken button in the Team menu, same as leveling:

Awakening a goddess will increase her number of stars:

The currency used for awakening is Soul Stones. They can be obtained by increasing the goddess' affection towards you, or from summons.