BJJ is both physical and mental chess. Although physically, strength and conditioning + nutrition is enough to prepare you for competition and improvement, what about the mental aspect?
In my opinion, mental toughness is something that will take you far in BJJ with that alone. It is not to be confused with the white belt who shows up and acts tough and spazzes out. Mental toughness is about giving your everything and striving tooth and nail to maximize your own potential. The people who already have mental toughness apply it to every single endeavor they decide to attempt. It has nothing to do with how good you are in relation to others, or who you can tap. It really comes down to "are you as good as you possibly can be".
Specifically for BJJ, I can list some instances that show this trait:
1) Showing up to class even when you just don't feel like it.
2) Not caring about losing but focusing intensely on improving.
3) Not tapping to moves that are simply painful but not threatening
4) Not tapping because you are just tired.
5) Not avoiding the toughest guy in the room because you don't want to get tapped.
Now an amazing motivational speech I see posted on facebook all the time.
Also a Navy Seal talking about his daily exercise