why do we use earth wire and explain its nature?

Answer 1

Hi. In amateur radio the earth wire (normally called a ground wire) provides a path for all the equipment to have a common electrical potential. It also helps keep antenna towers from building up a charge and aids in lightning protection.

Answer 2

I suppose you refer to the conductor "yellow/green" on your plugs.
It is used as a safety feature.
Conntected to the earth (ground), if the apparatus has a "leak" (electrical contact between the mains and the frame of the unit), the current will flow through the earth wire to the ground, and (hopefully) not through your body.
For an added protection, we also use "Residual Circuit Breakers" that will cut off supply if the current IN the unit if different (less) from the current returning from the unit.

Answer 3

Its a safety measure.

Depending on the design of the electrical device, it allows current arising from a fault or short to be directed safely to earth rather than through the user.

It is far less important in circuits that used residual current protection devices, and of no relevance at all for double insulated devices.