The Campaign menu is basically the main aspect of the game. 

It's where you can progress your story chapters. 

As you enter the menu, you can see there's an idle battle going on permanently there which racks up rewards as more time passes. You can collect those by tapping on the treasure hoard that appears. 

In order to advance in the story you can tap on Challenge, where a new battle chapter will ensue. 

The get stronger sub menu is where you can level up and improve your recruits.