I just got told:
Apparently 運動神経 means motor nerve:
運動神経が良い mean in this context? The conversation was about swimming, not something where reflexes are that important I believe.
A motor nerve is a nerve that carries command information out of the central nervous system (CNS) and toward effectors (muscles or glands) that will execute the commands.
Even if we take this definition literally, I think the expression ”運動神経が良い” is not too off. If we take motor nerve is good as transmitting information efficiently from CNS to muscles efficiently, I think it applies to real movement in sports.
運動神経 = motor nerves, reflexes
運動神経がいい = motor nerves, reflexes are good
Speaking of physical abilities, if your motor abilities or reflexes are good, chances are that you're the athletic type. It does take a good amount of reflex and reaction whenever playing a sport, especially for competition's sake.