The live wire is at high potential difference, while the neutral wire is at zero potential difference. When the switch is turned off, the electrical appliance will still be at high voltage, since the electrical appliance is still connected to the electrical mains via the live wire.

The electrical appliance being ‘live’ even though the switch is turned off is potentially hazardous as it increases the risk of electrocution and overheating and electric fire if a path to a lower potential difference is established.