I'm now on the objective "raise the special stats of 7 dwellers". What does SPECIAL mean?

"SPECIAL" means:

Strength

Perception

Endurance

Charisma

Intelligence

Agility

Luck

You will need to build a training room and put dwellers in there to increase one of their stats. There is a specific room for each SPECIAL stat. For the objective to be completed, you need to train 7 individual dwellers one time, not one dweller 7 times.