why does the colour of copper sulphate solution change when an iron nail is dipped in it?

The cour changes because of displacement reaction.

The reaction is Fe(s) + CuSO₄ (aq) FeSO₄  (aq)+ Cu (s)

                             Grey       blue                            green           brown

                                           solution                     solution

This happens because iron is a more reactive element than copper. That is iron comes above copper in the reactivity series. So, iron being a more reactive element than copper dispalces copper from its salt solution ( copper sulphate) and forms iron sulphate and copper metal is formed.

SO the colour of the solution changes from blue to green and a brown deposit of copper is deposited.