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The wire that is connected to ground pin of a plug is connected to the metal body of the equipment.Any leakage current appearing on the metal body of the equipment must be discharged safely to ground so the user do not get any electric shock when using the equipment.If there is any serious fault on the equipment, it also makes the fuse blow, saving the user. 

The pin of earthing is longer so when you insert the plug, the earth connection is made to the equipment first.When you remove the plug, the earth connection is removed last.It is bigger so you can not insert the plug in any other way. The smaller pins on the plug can go into the larger hole, but the larger pin will never go into a smaller hole. So any live wire cannot be connected to the body of the equipment.This is for user safety.