V̇O2max is the maximum rate of oxygen consumption that the body's cardiovascular system can maintain. Let's break that down:
When a muscle contracts, oxygen is required in the reaction that provides the energy. If we jump on a treadmill, and increase the speed or incline every couple of minutes, we will see the rate of oxygen uptake also increase -- to a point.
Oxygen is provided by the "cardiovascular" system, meaning the heart and blood vessels. There is an upper limit to what the heart can provide. At V̇O2max, we might increase the speed or incline of that treadmill, but the heart and blood vessels can no longer provide any more oxygen.
Why does this provide a measure of fitness?
The point of exercise (or one of the points including mental health...etc) is to stress the body in such a way that in the process of trying to maintain homeostasis (I will get to that in a second), the system adapts in such a way that it can provide more capacity in the future. Think muscles getting bigger due to weight lifting, or brisk walks / runs getting easier over time.
A key to understanding adaptation is the idea that the body has systems that keep its systems 'in working parameters' for safety, like the systems in a Tesla that keep the battery from dangerously overheating. For example when the muscles demand more oxygen due to increased effort, the body works to maintain the level of oxygen in the blood by increasing heart and respiratory rate (probably chiefly in order to protect the brain if I had to guess.). This puts a stress on the heart, to which it adapts over time.
Locally, Rutgers will test V̇O2max in a lab for less than $200. Fitness watches also have a test that uses heart rate variability, a subject for a future discussion, once I understand it, as a proxy for maximum oxygen uptake.
--edit: One potentially useful note is that V̇O2max occurs at max heart rate, so if something is calling for exercise (as in a stepped test) at 85% of V̇O2, this is the same as 85% MHR.
-- Note to self: The dot above the V in V̇O2max reflects the fact that it is a rate, and is typed by using the extended US keyboard on a mac and the key combination opt-shift-w after the letter.
