What is there in this 3D representation of organic molecules I fail to grasp?
You have drawn the compounds correctly, and yes 


a solid wedge means the bond is coming out of the plane of the screen towards you
a dashed wedge means the bond is going behind the plane of the screen away from you
a solid line means the bond lies in the plane of the screen


Here is a Newman projection of your molecules, sometimes Newman projections can make it easier to "see" things.



Build a model (I did) or flip the drawings around, there is no way you can interconvert the isomers labeled "S,S' and "R,R"; they are chiral enantiomers.  The meso compound and its mirror image are easily converted into one another (try rotating the molecule about a $\ce{C_2}$ axis that lies in the plane of the screen, 2) is perpendicular to the mirror plane [the dashed line in my drawing] and 3) bisects the $\ce{C_2-C_3}$ bond in the molecule); they are indeed representations of the same molecule.