"Intelligence is quickness in
seeing things as they are."
-George Santayana
Motion Offense Execution: The sooner you learn to read the defense and not worry about where the ball is, the better offensive player you will become. It takes discipline and intelligence to "things as they are" on the floor.
Good Individual/Team Defense: This is also the ability to see what is unfolding on the court -- understanding where the ball and your man is at the same time as well as the ability to anticipate screens and cuts.
Roles: You could actually change the wording a bit by saying "Intelligence is quickness in see YOURSELF as you really are." This may be one of the most difficult things for players to do.
Recruiting: It is important that coach can quickly yet accurately understand the ability of a potential student-athlete but also that's players ability to fit in with your system, your method of teaching and the chemistry of your team. In many cases, you must also "see things as they are" in terms of whether you can successfully recruit that particular player.
Game Adjustments: The quicker you can ascertain the success or lack thereof in regard to a game plan, the more effectively you can make the necessary adjustments to help your team succeed.
Practice: The best coaches have a great feel for what is needed in practice on a daily basis. They know when to pull back to save legs...they know when to push forward to develop toughness.
Relationships: Each person in your "family" is different. They were raised differently -- coached differently. They have various motivating factors. The "quicker" you "see THEM as they are" the better you will be able to communicate and build trust.