mind-body relationship “finding a place for the mind in a world that is fundamentally physical” 

—has been puzzled over for centuries, and is unlikely to be resolved any time soon. The reason is that apparently every possible solution has inadequacies. Anyone familiar with the philosophical literature is aware of all the problems with Cartesian substance dualism, reductive physicalism, eliminative materialism, behaviorism and functionalism, non-reductive physicalism and emergentism. One is tempted to agree with Colin McGinn that the cognitive apparatus of humans is intrinsically inadequate to the problem of explaining the relation between the mind and the brain.  How something like consciousness can emerge from something like the brain seems totally inexplicable.

What is the Buddhist explanation for Mind-Body problem?
I think the problem stems from a desire to know the mechanistic workings of reality; e.g. how one thing affects or effects another, rather than simple that it does so.  Buddhism is, for the most part, terribly devoid of explanations about the former, since it is ultimately a practical path. As the Buddha said time and again,

Bhikkhus, both formerly and now what I teach is suffering and the cessation of suffering.
-- MN 22 (Bodhi, trans)

In the context of your question, as others have pointed out, there really isn't any problem on the surface: physical reality clearly exists, as does mental reality; they also clearly interact with each other in a manner that is fairly easily definable.
The problem comes when you try to know more beyond these simple facts, i.e. how and why they exist and interact the way they do. These questions are foreign to Buddhism because they are not really useful at all, and moreover are probably ultimately outside of the realm of what can be empirically known.