Question

what does a harmonic function mean physically?

Answer 1

depends on what the function describes. It can mean many things

Answer 2

f sub xx+ f sub yy = 0

Answer 3

this is a Laplace equation. It is used a lot fro example in electrostatics. If it vould describe a potential in a región it means that there is no net charge inside

Answer 4

also you could say that it obtaint it's máximum on the borders of the región.
Also, that the value at the point inside of the región is the average of the values on the border.