Is potential energy an energy exists or potentiality of energy? I want to ask whether Potential Energy is truly existing Energy - though i know the energy concept is abstract and we do not know what is energy truly as Feynman said - or it is the potentiality that the body will gain energy in the future , i do not mean to be philosophical question but really i want to know that point, and if we can give the potential energy concept away and formulate the laws in other way ? 
 A: I see the viewpoint you're coming from. From the wording of "potential energy", it sounds like the energy might not exist until it becomes kinetic energy. Potential energy is as real as kinetic energy though. The idea is that the energy gets stored in the fields that produce the force, and that the energy is transferred between kinetic energy and field energy. This is most evident in electromagnetics. Common electronic components, capacitors and inductors, store energy in electric and magnetic fields respectively.
The picture with gravity gets more complicated though, because gravity is described by general relativity, which does away with energy concepts. It's not really my field, so I can't comment further than that.
Edit: To answer, "Do the fields really exist, or are they a just a mathematical tool?", yes, they do exist. Light for example, is an electromagnetic wave, which can transfer both energy and momentum. In a quantum mechanics view, this is a discrete particle known as a photon, which interacts similarly to any other particle. As an assurance that photons are real, there's something known as pair production: high energy photons can spontaneously form pairs of particles such as electrons and positrons. At this point, I would believe that the fields are as real as electrons and positrons.
Alfred Centauri's comment is also a good answer as to why we think the fields are real.
A: Well your question was not perfect, but acceptable. the idea of energy may sound easy, but deeply it is a very strange Idea.
but the answer to your question: no it doesn't mean it "potentially" gonna gain. I see that you read Feynman's lectures, that's very good, but these speeches actually are for people who accepted the idea of energy blindly, and didn't think hard enough to see how abstract it could be.
See it is just the matter of modeling. we model the world around us in the "matter and energy" phenomena. there is something named Energy that let the objects move. that's the first clue of the energy! but we will encounter with a problem:
Imagine a you are holding the ball in the air. it is not moving, so we say"Okay it doesn't have any ENERGY right now" but as soon as you let it go it start to move! but how? it gained energy some how. from where?
this is when the potential energy comes to the mind. when you grab the ball and raised it to a level, some energy is stored inside! some energy that is potential in it and ready to go out of the object as soon as you let the ball go. this potential energy in this example is called Gravitational potential energy . because it is due to the gravity.
but the potential energy can be used in so many places. like electrical potential. generally a moving object has energy. the energy that the object has due to it's movement is called Kinetic energy with the sign of $k$ . but for a non-moving object it doesn't mean it doesn't mean that it doesn't have any energy. there is some energy stored Inside the object that we call Potential energy and we show it with letter $U$ .
and the most famous equation is this : $E=U+k$ . and it means any mechanical energy that an object is the sum of energy inside and the energy due to it's movement! and we can say the total amount of energy doesn't change.
the energy turns from inside energy to kinetic or another way around, but it never changes. 
so the word potential is for"potential to move". the energy that is stored inside the object that we can not see.
