When zinc is placed in copper sulfate solution, zinc displaces copper. The ionic equation is Zn + Cu2+ → Zn2+ + Cu.
Each zinc atom loses two electrons to become a zinc ion, Zn2+. Oxidation is the loss of electrons, so zinc is oxidised. Each copper ion, Cu2+, gains two electrons to become a copper atom. Reduction is the gain of electrons, so copper ions are reduced.
The electrons lost by the zinc are the electrons gained by the copper ions, so oxidation and reduction happen together. A reaction in which both happen is a redox reaction. In a displacement reaction the more reactive metal is the one that is oxidised.