What is the electric potential at a point? 1) What does the electric potential at a point exactly mean? My teacher tells me that current flows from higher potential to lower potential but when I ask him the reason, he fails to give me a convincing answer. 
2) And can anyone explain how electric potential is related to potential energy & work done?
3) Further, when I referred a Physics textbook it said that since Coulomb's force & Gravitational force are mathematically similar, electric potential is a charge's equivalent of a the potential energy of mass. Hence I related Electric potential to the potential energy of a ball for example. A ball falls from a height to the ground because of Potential energy- so similarly, current flows from higher to lower potential. Is this analogy correct?
Even if the above analogy is correct, I still cannot understand why current flows between two electrodes of an electrochemical cell. The only explanation my teacher offers is that there is a potential difference & thus current flows from higher to lower potential. This explanation is not of any help since I don't understand what potential is in the first place!
4) If the analogy is valid, then how do the electrons in the Electrochemical cell move without an electric field to impart the electric potential energy? (as in gravitational energy where the potential energy is present only if gravitational force is present? In space, no object of any mass has weight)
 A: I would advice you to read the wikipedia article on electrochemical cells.
You will see that there, chemical energy is transformed to electrical energy, i.e. a collective electric field is generated from all the molecules participating in the chemical reaction. Thus the analogy with the gravitational field is valid.
The energy comes from the chemical action, and in rechargeable batteries from the charging circuit. A charged battery has a potential difference between its two poles so that when a light bulb, for example, is introduced, the electrons in the wires move  towards the least potential and on the way light the bulb because of the resistance they encounter.
A: If we take electrical potential then 

the electric potential at a given point is the magnitude of potential
  point at that point per unit charge.

But a much better definition is:

electric potential at a point is defined as the amount of work done in
  moving a unit positive charge from infinity to that point.

following this

potential difference between two points is defined as the amount of
  work done in moving a unit positive charge from one point to the other
  against the field

I assume you got the connection between potential and work done
since Coulomb's force & Gravitational force are inversely proportional to the square of the distance, it has been stated that  Coulomb's force & Gravitational force are mathematically similar
Now coming to the part why current flows from higher potential to lower potential, 
In nature all system wants to attain minimum energy because lesser the energy more is the stability (that is why atoms in excited state quickly attain ground state releasing energy)  similarly current(which is nothing but flow of electrons) want to flow from a higher potential
A: Electric potential is the potential energy per unit charge that a charged object would have at a point in space. The electric field points in the direction of the potential gradient, so objects feel a force down a potential gradient, the same as water feels a force downhill. Water goes downhill, so charges go down a potential gradient. To go up requires energy.
The electric potential is a fundamental quantity in the electromagnetic field. It is defined by the property that it is the potential energy per unit charge. The concept cannot be reduced further.
A: the potential at a point  A  is equal to the charge  in  electric potential energy per unit test charge when it is moved from the reference point to the point A.
