The game tasks you with giving them gifts, you have to earn 3 stars with them by giving gifts they'll like. You'll also need to make sure to have the heart icon next to the gift option, this indicates how close the bond is and there's a hidden score based on what type of gifts you give. The ! indicates that the next chapter is ready to go (if you don't see the ! then that means it might need to happen in a different location or a different time.
You level up the girls by taking them on dates that this increases their weekly/monthly profit that you can claim and also unlocks new outfits and potentially new post-story H-scenes.