To me, we are all "athletes", but I know that at the elite level of sports, a special confluence of factors must come together for an evaluator of elite talent to stamp us with the anointed label of "athletic".
I suspect the major factors include:
1) Exquisite Proprioception
2) Elite genetic ability to generate power and or endurance
3) Desire to execute
4) Intuition or "feel" for the sport-how the brain is wired to respond to the stimulation of the sport
The teachable factors:
1) Proper strengthening and conditioning
2) Proper rest and nutrition
3) Optimal mechanics
4) How to play and play intelligently ie: make good decisions
The talent evaluator looks at the top list when determining if it's worth their time to execute the bottom list.
Assumimg desire and intuition, the athlete factors boil down to proprioception and elite genetic physical ability.
Some people have great Proprioception, but lack the genetic physicality to generate the proper response. Some people have great genetic physical ability, but average proprioception.
An "athlete" in high velocity sports that require painstaking precision and accuracy will have both. The ones termed "athletic" will have both to a greater degree as well as learned a few of the teachable factors listed.
When watching their bodies in these situations, the elite talent evaluator is seeing the body finitely aware and reacting with great force and precision. It stands out when you're near it, as I'm sure was obvious with every great athlete. It's fairly common to run across these athletes, but they do not all succeed, because it takes more than just being "athletic".