Electricity can be dangerous in these situations:
damaged insulation
overheating of cables
damp conditions
Damaged insulation:
All electrical appliances require two wires to complete a circuit, the live and neutral wires, starting from the voltage supply to the appliance and back. These wires are insulated in rubber. Wear and tear from of cables and appliances eventually expose the wires. If the rubber insulation is also damaged, then there is a risk of attaining an electric shock.
Overheating of cables:
A short circuit or overloading causes a large current which overheat the cables. When a live wire comes in contact with a neutral wire it produces an electric shock.
Damp conditions:
When a live wire comes in contact with water then the water provides a conducting path for a current and maybe through a body. The human body can only withstand a current of up to 50mA.