A faculty refers to any of your mental or physical abilities. If you lose your faculties, you are powerless. The faculty of a school is comprised of the people who work there. Lose them, and you have a different kind of problem.
Faculty comes from the Old French word faculté, which means “skill, accomplishment, or learning.” You may have great faculties of memory, sight, mobility, charm, math, and musicality, but, as Beethoven was in the end, be robbed of your faculty of hearing. Any aptitude or ability — inborn or learned — that you have is a faculty. Also, if you go to school, your teachers make up the faculty of that school.