What is 'fitness' and does it matter?

The conventional meaning of the term 'fitness' is cardiovascular or aerobic capacity - the heart rate response to exercise.  In real-world exercise scenarios, e.g. sport, the heart rate response is actually a reaction to opposing variables: demand and supply.  Supply is aerobic power - the size and capacity of the gas tank.  Demand is how well you move or the energy 'cost' to complete a task.

Imagine two individuals in an exercise class.  One moves easily and displays a low level of physical discomfort or stress.  The other has much weaker motor skills, and moves with obvious discomfort.  We could say that the 2nd individual is much less fit than the first but that's actually not the problem.  The issue for any individual with weak or immature movement skills is cost.  Whatever capacity there is bleeds out quickly under physical duress.

So, the question becomes whether we can expect to get a better return by a) lowering demand or b) through raising supply?  The sensible answer is a) as all the capacity in the world is of little use to an inefficient machine - think of an beat-up old car with a modern, high powered engine and you will understand the pointlessness of the scenario.  In reality, only the highly trained and efficient may be limited by aerobic power.  

For most individuals, children and adults, the big impediment to sport or exercise performance is a weak or incomplete athletic toolbox: basic movement skill or structural deficits that impair physical performance under duress.  That is not to say that activity does not raise capacity.  It does.  The question is what's the optimal training target: stress (i.e. a high heart rate) or quality of movement.  High quality movement provides an excellent platform to safely and effectively develop capacity.