What is minimized in a generalized least squares regression?
The average error between a set of real points and a regression curve.
A regression is simply a type of line or curve that tries to correlate a set of points to each other. Because such a curve cannot "fit" (calculate to) each point exactly, the "best fit" to the given data is found by looking at the average distance of each actual point from the calculated regression curve.
A small "error" means it is a "good fit" of the data.