All classes take some sort of skill to master obviously, going to highlight a few skills you need to be a 'master' of a certain class.
Scout: Timing jumps, aim, positioning (put out the max damage while maintaining a safe distance)
Soldier: Rocket jumping, enemy prediction, rocket projection(as in where and precisely when the rocket will hid what you're aiming at), and positioning
Pyro: Awareness (for projectiles and spies), airblasting, flare projection (if applicable)
Demoman: Airbursting (unfortunately), grenade projection (same as rocket projection but with grenades), sticky jumping
Heavy: Awareness (spies and snipers, watching over your medic), prediction (anticipating when/where there will be enemies), positioning
Engineer: Awareness (spies), building positioning, building efficiency (how fast and efficiently you can start setting up/finish setting up)
Medic: Awareness (all oncoming damage against you and allies, spies+snipers), healing priorities, knowing when to run and when to fight, crossbow projection (if applicable)
Sniper: Awareness (of targets and spies), aim (obviously), positioning
Spy: Awareness (of what's happening around you, potential targets), aim, timing, prediction (anticipating when/where there will be enemies), positioning
Class(room) discussion: What class is the easiest to master and why?