I have read a bit about the torsion of an acyclic complex. One of my concrete hopes was that I could understand why $ L(7,1)$ and $ L(7,2)$ are not homeomorphic – I am under the impression that classifying lens spaces was I problem that motivated Reidemeister to introduce torsion.

All of the definitions of torsion that I have seen are totally opaque to me. How do people think of the torsion of a chain complex and how in trying to classify lens spaces could I have been led to defining/computing torsions?