Not sure if you're still interested in this post, so I will keep my answer brief for now. In short, the location of the indices indicate how the components of the given tensor transform under a change of basis in the underlying vector space. Lower indices indicate a covariant transformation; i.e., a change in the tensor's components that behaves in the same manner as the change of basis itself. Upper indices indicate a contravariant transformation; i.e., a change in the tensor's components that behaves according to the inverse of the change of basis itself.
This is likely to be a bit vague. I am happy to discuss the topic further if you're still interested.