The x,y pair of coordinates indicate the coordinates of the observed point, while the x',y' pair indicate the coordinates of the source of influence (let's say an antenna, for example).
Well, x' and y' (and z') are the scalar cartesian coordinates of a puntual source, not a whole antenna, but just a point.
If you wanted to calculate the influence of the whole antena, you should sum the influences of every point of the antenna, thus, you should integrate the green function across the x',y' and z' axes.