, I don't mind you making that point about how the term "impulse" has been mis-used by non-science types over the course of the Trek series ... but I'd thought that after such a long rant, you'd provide us with some explanation of what it does
Well, the short form is this:
The application of force over time.
So, apply a force to a known mass, and you get an acceleration. Apply an impulse to a known mass and you get a velocity.
You can get the same velocity imparted to the same mass by applying a high force for a short period of time, or a low force for a longer period of time. Because both apply the same impulse to the mass.
That's a very simple take on the concept, but it sums it up pretty well. If you want to know more... if you want to get into integrals and other somewhat more complex forms of math... you can do so, of course, but the general concept is as I've just described it.