Here is what I know about Landau-Ginzburg models:

It is an important player in the story of mirror symmetry.
It involves "potentials" which are functions of complex varibles, which have isolated singularities at the origin.
There is the notion of universal unfolding(miniversal unfolding, or miniversal deformation) attached to each of these functions.
One can attach the frobenius manifold structure to this unfolding.
One version of mirror symmetry is the isomorphisms between frobenius manifolds.

My question is:

Is there a good book or paper where I can learn about LG models? Especially mysterious to me is about the potentials. What is the physical motivations behind these functions?