An electric current is a flow of electric charge. Most mains powered appliances need three wires to work safely: live, neutral and earth.
Resistance (measured in Ohms) is a measure of how hard it is for a current to flow through a circuit component. The size of the current flowing depends on the potential difference (voltage) driving it and the amount of resistance it has to flow through.
In order to flow, an electric current needs:
An electric current is a flow of electric charge. Conventional current flows from the positive terminal of the power source to the negative terminal.
In wires charge is carried by negatively charged electrons. These are free to move from atom to atom in metals. They move in the opposite direction to the conventional current.
A lot of mains powered appliances need three wires to work safely. Only two of the wires are used when the appliance works properly. These are the live (brown) and the neutral (blue) wires. The live wire carries current to the appliance at a high voltage. The neutral wire completes the circuit and carries current away from the appliance. The third wire, called the earth wire (green/yellow) is a safety wire and connects the metal case of the appliance to the earth. This stops a fault making the case of the appliance live.
If a fault occurs where the live wire connects to the case, the earth wire allows a large current to flow through the live and earth wires. This overheats the fuse which melts and breaks the circuit.
Appliances such as hairdryers are said to be 'double insulated' and there's no need for an earth wire because the case is made of a non conducting plastic. If a faulty live wire touches the inside of the plastic case there's little risk as the case is an insulator.
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