What is there in this 3D representation of organic molecules I fail to grasp? I think there's a basic idea I'm missing about 3 Dimensional representation of molecules. I think it may be about converting to Fischer representation. Consider the following two products of bromination of an alkene, the first one being for cis-form and the 2nd one for trans-form.



I know the question may sound stupid, but it's crucial to get the basics. Why is the product II) the meso form and the products I) are the optically active forms. By what I know, the solid wedge goes towards the observer, so in product II), shouldn't the Bromine substituent(or maybe the $CH_3$ substituent) and $H$ atom be on the 'same side', making it the one optically active?
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.