Iron reacts with the SO42- ions to form FeSO4. It gets oxidised to +2 oxidation state.
Copper gets oxidised at the anode to form Cu2+ ions. These Cu2+ ions reach the cathode and get reduced to Cu atoms. The SO42- ions react with Fe2- to form FeSO4 and remain in the solution.
at anode: Cu(s) → Cu2+ + 2e-
at cathode: Cu2+ + 2e- → Cu(s)
Fe(s) → Fe2+ + 2e-
In the solution: Fe2+ + SO42- → FeSO4