For a localized charge distribution the potential is set to zero far away from the charge distribution (at infinity)
Now, when grounding a conductor, i.e. connecting it to Earth, it is said that we are setting its potential to zero.
Why Earth's potential is zero? And if it is zero, is it zero even if the potential is still zero at infinity?
Earth's zero potential is just an arbitrary point similar to (0,0) of co-ordinate system. It has been chosen for Engineering practices because it has very very low theoretical potential (in light with charge at Infinity) and it's easily accessible to everyone and adding charge to it doesn't change it's theoretical potential. With reference to this arbitrary point, potential of wiring things are rated. It's similar to why we use sea level to measure height. Remember, sea level also has height from many reference points such as Earth's core, but we take it zero for many practices.
For electrical engineering purposes, Voltage is a potential difference with respect to a reference point. Absolute electrical potential is meaningless in electrical engineering contexts because circuits involve electrical current flowing from a high-potential point to a low-potential point and not to a no-potential point. Therefore electrical engineers talk about Voltage and not electrical potential. When you read "setting its potential to zero" what is really meant is "setting its Voltage (its potential difference) to zero with respect to the Earth". The former is simply a short form that is usually understood unambiguously to mean the latter in electrical engineering contexts.
Earth is simply a commonly used reference point. However, to add to the confusion, the electrical potential of Earth is not the same everywhere. One end of your street could have an excess of electric charge with respect to the other end of your street, so if you grounded two different circuits on each end of your street and connected them together, you could end up with this charge flowing from one circuit to the other. This can pose problems such as electrical noise between equipment that must be connected together but may not be grounded at the same point. This effect is referred to as a ground loop.
Your Earth may not be equal to my Earth, but as long as you always use the same Earth, you will always be using the same reference point, and you can simply call it 0V. It's a convenience thing.
If we assume potential at infinity to be zero and Earth to be spherical then the potential at the surface of the earth is given by ${kq}/{r}$, where $k$ is a constant, $q$ is the charge on earth and $r$ its radius. As $q$ is extremely small and $r$ very large, the potential at Earth's surface is almost zero. So for all practical purposes we assume its potential to be zero. The potential at infinity is assumed to be absolutely zero whereas that on Earth's surface almost zero.
Generally , at any given point ,the electrical potential is measured with respect to another reference point . The other point can be anywhere and the reference point is assumed to be at zero volt relative to itself . In most of the electrical applications ., reference point is assumed to be the earth.
Radius of earth is large with respect to conducting body so its potential is very low wrt conducting body hence we assume potential of earth is 0
It is helpful to say we can't measure a potential, only a difference of potential between two points. We call that a voltage.
Voltage notion is interesting because:
Note earth potential is not constant, and --something at first thought unbelievable-- potential increases in atmosphere by about 100 V with each meter of altitude. Of course the voltage between hour head and our feet is null because our body is a relatively good conductor, but a plane at an altitude of 40 km is at a potential of about 400 kV. Thrilling.
Actually the potential gradient also varies a little bit. So... as everything varies, where should we put the reference?
The answer is: It doesn't matter where the reference is, but earth surface is nearly equipotential and so is a handy reference for comparing potential everywhere on it.
With this reference, the potential looks like this, without and with a person standing on earth surface:
No need to mention where the preferred path for lightning is.
