What is Heroes Hall used for?

Heroes hall is the building where you recruit heroes, using the daily free tickets and others that you earn (or buy). You can also use the token shop to unlock heroes if you are earning hero tokens. Upgrading the building increases the amount of Exp your heroes earn from activities.

The military academy building is for exchanging hero medals into wisdom medals. The heros medals come from recruiting duplicate heroes. They are used to unlock some hero skill and also exchange for wisdom medals that you need to unlock and upgrade hero skills.

Exchanging will costs you money as well as the medals. But you will need to do it when you can to keep gaining the wisdom medals.