I would really appreciate if someone could explain.

What does a correlation function like a density-density correlation function $$C_{nn}(\vec x_1, \vec x_2)= \langle n(\vec x_1) n(\vec x_2)\rangle$$ measure, or what does it mean as a function.

And even more important how does it do this. If someone could explain this in general terms general functions of randomly variables it would be very helpfull.

I know about this question but none of the answeres really describes what generally a correlation function signifies or how it does this mathematically. But this is exactly what i need to know.