From an introductory mathematical economics textbook:
The derivate of TR is actually a proper definition of marginal revenue; the 1-more-unit approach of introductory economics is only necessary because many introductory students lack the mathematical background to appreciate the calculus definition.
get it? ie the real world explanation is just because you dumbos don’t understand mathematics.
I’ll explain- I had to suffer through this in public education- TR is total revenue(of selling a product) and the one-more-unit is the graphical repreentation of this line, soo as the derivative(slope of a curve at a point) is the value added to said curve at said point.