At the Academy you can improve your hunters by teaching them skills, traits and secret tech. These things are really important as they will strengthen your hunters, just as better weapons and armor would. Here is a little bit about each of the three things that can be done at the Academy.
Traits are learned at the academy, and they offer incredible buffs to individual hunters. The only catch is to level up any trait costs Reincarnation points, and you only get these by reincarnating hunters. So spend your reincarnation points wisely. Also, you will need to remember to keep leveling up your academy to unlock more trait upgrade options. Reincarnation points can only be spent on hunters that earned that specific reincarnation point.
Skills are learnt at the Academy, and are different for each class of hunter. To learn new skills, tap the hunter and select learn > skill . Then tap the speech bubble when the hunter arrives at the Academy. Now you cans see the available skills that can be taught to this hunter. For more skills to be unlocked you will need to upgrade your Academy.
You can teach hunters Secret Techniques at the Academy, you can allocate all of your secret technique books to any hunter that you want. You get Secret Technique books when a new hunter arrives. Secret Techniques are other powerful upgrade options for your hunters which you should do so they become stronger.