When iron nails are added to an aqueous solution of copper sulphate, a displacement reaction occurs in which iron displaces copper from its solution which leads to fading of the blue colour of solution. After some time, the displaced copper settles down on the iron nails and reduces the surface available for reaction. So, the iron nails do not dissolve completely. The reaction involved is:
$\text{Fe}\text{(s)}+{\text{CuSO}}_4\text{(aq)}\to {\text{FeSO}}_4\text{(aq)}+\text{Cu (s)}$