In electrolysis, ions are turned into atoms or molecules by gaining or losing electrons. At the cathode, positive ions each gain electrons. At the anode, negative ions each lose electrons. We show each change in a half equation, which shows one electrode on its own and includes the electrons.
At the cathode in molten sodium chloride: Na+ + e- → Na. Each sodium ion gains one electron. At the anode: 2Cl- → Cl2 + 2e-. Two electrons are released for each molecule of chlorine. The overall equation is 2NaCl → 2Na + Cl2.
Other half equations to know: Cu2+ + 2e- → Cu, where a copper ion with a charge of 2+ gains two electrons to form a copper atom; 2H+ + 2e- → H2 at the cathode; and 4OH- → 2H2O + O2 + 4e- at the anode. In every half equation the charges on each side must be balanced, and the electrons gained at the cathode equal the electrons lost at the anode.