Faculty is a statistic representing the size of each army. At level 15 you build a barracks from which you can either conscript troops using crops (8 troops per 1 crop), or use volunteers (limit 10 uses a day, cool down of 30 minutes).  And after lvl 16 you start losing faculty, although the specific number lost depends on many things
What do they do?Edit
Faculty is the population of your army. The higher your faculty the more damage they can withstand. Faculty can be increased by enhancing your equipment, increasing your heroes level, and at your academy.
Most players stop at level 15 and upgrade their barracks and recruit troops until their faculty reserve is totally full. At level 15 and higher you begin to use your reserve of faculty, this means if you lose a battle you also lose the amount of soldiers that entered the battle. If you have a narrow win you will lose most of your faculty. Keeping your reserve up is important because without it you will lose all of your battles because your armies faculty will be too low or 0. Always make sure to conscript or volunteer often.