The earth wire connection to ground
Connecting the earth wire to ground
The earth wires from all the electric sockets in your house often end up in one thick earth wire which is connected to a big metal spike or plate driven into the ground just outside your house. Sometimes all the earth wires from several houses are joined like this.
This makes an electrical connection between anything connected to an earth wire, the body of your metal kettle, for example, and the planet.
Damp earth has a pretty low resistance. Remember the resistance of a wire is low if it's wide. The earth around your house is very wide indeed so it's easy for an electric current to flow in it.
We say the ground is at 0 V. In other words an electric current won't transfer energy away from the ground, only to it.
Where does the current go?
In an AC circuit the current doesn't go anywhere anyway. It just oscillates back and forth. So if there's a current in the earth it just consists of wobbling charges.
With a DC earth you don't worry about where the electrons actually end up. You just accept that the ground (i.e. the planet) has a huge capacity to accept or lose electrons in one place because they'll all be balanced out in another place.
In other words the total number of electrons in the planet is fixed and all you can do is shift them around. Because the resistance of the ground is so small this balancing movement comes at very little cost in energy.