When there is an alternative low resistance path for the current to flow through, the current will by pass the other path that has a resistance load (e.g. resistor or bulbs). This is called a 'short circuit' and usually the current will be higher.

High power electrical appliances are those which draws high current. The thinner the wire (smaller cross-sectional area), the higher the resistance of the cable which brings the current into the electrical appliances.   More thermal energy will be generated due to this higher resistance in the cable. The cable might be too hot or catch fire. So it is advisable to have thicker cables for high power electrical appliance as thicker cables have lower resistance.