The change in colour of copper sulphate solution when an iron nail is dipped in it is due to the process of displacement reaction. This reaction involves the replacement of one metal by another in a compound. In this case, the iron nail reacts with the copper sulphate solution to form ferrous sulphate and copper.

The chemical equation for this reaction is:

$$Fe(s) + CuSO_4(aq) -> FeSO_4(aq) + Cu(s)$$

Here, iron (Fe) displaces copper (Cu) from the copper sulphate solution. As a result, the blue colour of the copper sulphate solution fades, and a green colour appears. This green colour is due to the formation of ferrous sulphate.

This displacement reaction occurs due to the difference in the reactivity of iron and copper. Iron is more reactive than copper, so it can replace copper from its compounds. This reaction is also an example of a redox reaction, where iron undergoes oxidation and copper undergoes reduction.