VMG means made good to the target destination, so it only has meaning in the context of a GOTO, whether electronic, in your GPS or manual on your chart.
Speed = Distance div. by Time.
So VMG = Distance towards target/Time taken to go that far.
If you are pointing away from the target, due to tacking for instance, or tide, then you must multipy the water speed travelled by the cosine of the angle your water track deviates from the required ground track.
So if you make two miles in quarter of an hour, but are on a line which is pointing 24deg away from destination, you will have speed = 8kts, VMG = 8cos24 or 7.3kts.
The term "VMG" was in use long before the arrival of GPS, and may still be used in the original way as meaning "speed made good to windward". It's a very useful concept, allowing you to balance off the increase in speed and reduction of leeway resulting from bearing away a few degrees against the loss of speed and increased leeway resulting from pinching up to the wind.
One:: VMG = Velocity made good (not VECTOR).
The point about velocity is that it is a vector quantity, i.e. it has magnitude and direction. So the velocity in the direction you actually go through the water (or air, same problem with flight), V, is resolvable into one component in the direction you want to go (cosV) and another at right angles (sinV) (aka the quadrature component, if you want to be sassy).
Two:: My posting was absolutely clear, and did not rely on GPS existence. I pointed out that VMG depends entirely on the direction you want to go, easily related to GPS and GOTO.
Three:: VMG measurement and usage was not what the posting asked for, but I agree that a principal use of a measurement is to be able to directly read out whether cracking off a bit is actually increasing VMG as well as boat-speed.
Four:: It is also useful when you are on passage and need to keep a certain speed to keep to your plan, indicating when you should put the iron sail up so as to make the next WP in time for a critical flood tide into the estuary instead of arriving a bit later to face a fierce ebb and so stand off and on for 4 or 5 hours.
It never meant speed made good to windward. Speed is not a vector quantity.
You must define the direction of windward, then, even if the wind varies in direction from then on, your VMG is the velocity made good in the originally defined direction.
Now, it is entirely reasonable that a meter can be instantaneously be measuring the true direction (by apparent wind direction and water speed) and computing the instantaneous VMG accordingly, and it would be measuring speed made good to windward (but notice, NOT speed made good to the windward mark!). But such a meter doesn't change the definition. And keep bearing in mind that there are other uses of true VMG (determining favoured tack, leebow effect).
Incidentally, GPS is NOT in itself that sort of really useful meter, as it only gives VMG in relation to a defined direction.
I don't know how far back you go, but before the days of GPS, Decca, etc, VMG meant the rate of progress towards the direction the wind was coming from; i.e. speed made good to windward. The direction component of the velocity vector was provided by the wind direction.
As an example, in "The Symmetry of Sailing" (Ross Garrett's excellent book on the physics of sailing) the list of symbols in Appendix A gives Vmg as "component of boat speed contrary to wind direction (speed made good)". His Section 3.4 gives all the relevant equations.