Question

what is the theory behind the chemical reaction of an iron nail with an aquoues copper sulphate solution

Answer 1

Fe(iron) +CuSo4(aqueous copper sulphate) gives FeSo4(ferrous copper sulphate) +Cu(copper)

Answer 2

Displacement reaction.
When iron nail placed​ in the CuSO4 solution . iron displace Cu.
Reaction
Fe+CuSO4------+Cu+FeSO4