Why do displacement reactions occur?
It is due to that zinc is more reactive than copper which is less reactive metal so, zinc can easily displaces copper from its solution. We can understand it as zinc ion, $\ce{Zn^2+}$ ion form more strong electrostatic attraction with sulphate ion, $\ce{SO4-}$ ion. 

Also, we can also consider the electrochemical series or activity series to give a better reason for the same. In activity series, zinc has greater value of standard reduction potential than copper's standard reduction potential value. It means, zinc can easily reduce Copper and it get oxidised. 

$$\ce{Zn(s) + CuSO4(aq) -&gt; ZnSO4(aq) + Cu(s)}$$